https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Feldman&feedformat=atomMath - User contributions [en]2018-06-19T06:44:43ZUser contributionsMediaWiki 1.26.0https://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15559Colloquia2018-06-18T06:48:05Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2018 ==<br />
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|Sep 12, 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguish Lecture series<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
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|-<br />
|Sep 28<br />
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|Oct 5<br />
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|Oct 12<br />
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|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
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|Oct 26<br />
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|Dec 7<br />
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|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|}<br />
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== Abstracts ==<br />
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=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
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Abstract: <ABSTRACT><br />
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== Past Colloquia ==<br />
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[[Colloquia/Blank|Blank]]<br />
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[[Colloquia/Spring2018|Spring 2018]]<br />
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[[Colloquia/Fall2017|Fall 2017]]<br />
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[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
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[[Colloquia/Spring2016|Spring 2016]]<br />
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[[Colloquia/Fall2015|Fall 2015]]<br />
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[[Colloquia/Spring2014|Spring 2015]]<br />
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[[Colloquia/Fall2014|Fall 2014]]<br />
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[[Colloquia/Spring2014|Spring 2014]]<br />
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[[Colloquia/Fall2013|Fall 2013]]<br />
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[[Colloquia 2012-2013|Spring 2013]]<br />
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[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Blank&diff=15448Colloquia/Blank2018-04-20T15:19:20Z<p>Feldman: </p>
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<div><br />
== semester==<br />
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|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
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|-<br />
|Sep 28<br />
| Gunther Uhlmann (Univ. of Washington)<br />
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|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|}<br />
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== Abstracts ==<br />
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=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
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Abstract: <ABSTRACT></div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Blank&diff=15447Colloquia/Blank2018-04-20T15:14:16Z<p>Feldman: </p>
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<div><br />
== semester==<br />
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{| cellpadding="8"<br />
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|Sep 21, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gunther Uhlmann (Univ. of Washington)<br />
|[[# TBA| TBA ]]<br />
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|March 4<br />
| Vladimir Sverak (Minnesota)<br />
|[[# TBA| Wasow lecture ]]<br />
| Kim<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT></div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Blank&diff=15446Colloquia/Blank2018-04-20T15:11:39Z<p>Feldman: </p>
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<div><br />
== semester==<br />
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{| cellpadding="8"<br />
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|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gunther Uhlmann (Univ. of Washington)<br />
|[[# TBA| TBA ]]<br />
| Li<br />
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|-<br />
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|March 4<br />
| Vladimir Sverak (Minnesota)<br />
|[[# TBA| Wasow lecture ]]<br />
| Kim<br />
|<br />
|}<br />
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== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT></div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=15433PDE Geometric Analysis seminar2018-04-19T00:34:20Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2018 | Tentative schedule for Fall 2018]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Spring 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|January 29, '''3-3:50PM, B341 VV.'''<br />
| Dan Knopf (UT Austin)<br />
|[[#Dan Knopf | Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons]]<br />
| Angenent<br />
|- <br />
|February 5, '''3-3:50PM, B341 VV.'''<br />
| Andreas Seeger (UW)<br />
|[[#Andreas Seeger | Singular integrals and a problem on mixing flows ]]<br />
| Kim & Tran<br />
|- <br />
|February 12<br />
| Sam Krupa (UT-Austin)<br />
|[[#Sam Krupa | Proving Uniqueness of Solutions for Burgers Equation Entropic for a Single Entropy, with Eye Towards Systems Case ]]<br />
| Lee <br />
|- <br />
|February 19<br />
| Maja Taskovic (UPenn)<br />
|[[#Maja Taskovic | Exponential tails for the non-cutoff Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|February 26<br />
| Ashish Kumar Pandey (UIUC)<br />
|[[# | Instabilities in shallow water wave models ]]<br />
| Kim & Lee<br />
|- <br />
|March 5<br />
| Khai Nguyen (NCSU)<br />
|[[#Khai Nguyen | Burgers Equation with Some Nonlocal Sources ]]<br />
| Tran<br />
|- <br />
|March 12<br />
| Hongwei Gao (UCLA)<br />
|[[#Hongwei Gao | Stochastic homogenization of certain nonconvex Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
|March 19<br />
| Huy Nguyen (Princeton)<br />
|[[#Huy Nguyen | Compressible fluids and active potentials ]]<br />
| Lee<br />
|-<br />
|March 26<br />
| <br />
|[[# | Spring recess (Mar 24-Apr 1, 2018) ]]<br />
| <br />
|-<br />
|April 2<br />
| In-Jee Jeong (Princeton)<br />
|[[#In-Jee Jeong | Singularity formation for the 3D axisymmetric Euler equations ]]<br />
| Kim<br />
|- <br />
|April 9<br />
| Jeff Calder (Minnesota)<br />
|[[#Jeff Calder | Nonlinear PDE continuum limits in data science and machine learning ]]<br />
| Tran<br />
|- <br />
|April 21-22 (Saturday-Sunday)<br />
| [https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]<br />
|[[#Midwest PDE seminar | ]]<br />
| Angenent, Feldman, Kim, Tran.<br />
|- <br />
|April 25 (Wednesday)<br />
| Hitoshi Ishii (Wasow lecture)<br />
|[[#Hitoshi Ishii | Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory]]<br />
| Tran.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Dan Knopf===<br />
<br />
Title: Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons<br />
<br />
Abstract: We describe Riemannian (non-K&auml;hler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking K&auml;hler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-K&auml;hler solutions of Ricci flow that become asymptotically K&auml;hler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of K&auml;hler metrics under Ricci flow.<br />
<br />
===Andreas Seeger===<br />
<br />
Title: Singular integrals and a problem on mixing flows<br />
<br />
Abstract: The talk will be about results related to Bressan's mixing problem. We present an inequality for the change of a Bianchini semi-norm of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which one proves bounds on Hardy spaces. This is joint work with Mahir Hadžić, Charles Smart and Brian Street.<br />
<br />
===Sam Krupa===<br />
<br />
Title: Proving Uniqueness of Solutions for Burgers Equation Entropic for a Single Entropy, with Eye Towards Systems Case<br />
<br />
Abstract: For hyperbolic systems of conservation laws, uniqueness of solutions is still largely open. We aim to expand the theory of uniqueness for systems of conservation laws. One difficulty is that many systems have only one entropy. This contrasts with scalar conservation laws, where many entropies exist. It took until 1994 to show that one entropy is enough to ensure uniqueness of solutions for the scalar conservation laws (Panov). This single entropy result was proven again by De Lellis, Otto and Westdickenberg in 2004. These two proofs both rely on the special connection between Hamilton--Jacobi equations and scalar conservation laws in one space dimension. However, this special connection does not extend to systems. In our new work, we prove the single entropy result for scalar conservation laws without using Hamilton--Jacobi. Our proof lays out new techniques that are promising for showing uniqueness of solutions in the systems case. This is joint work with A. Vasseur.<br />
<br />
<br />
===Maja Taskovic===<br />
<br />
Title: Exponential tails for the non-cutoff Boltzmann equation<br />
<br />
Abstract: The Boltzmann equation models the motion of a rarefied gas, in which particles interact through binary collisions, by describing the evolution of the particle density function. The effect of collisions on the density function is modeled by a bilinear integral operator (collision operator) which in many cases has a non-integrable angular kernel. For a long time the equation was simplified by assuming that this kernel is integrable (the so called Grad's cutoff) with a belief that such an assumption does not affect the equation significantly. However, in the last 20 years it has been observed that a non-integrable singularity carries regularizing properties which motivates further analysis of the equation in this setting.<br />
<br />
We study behavior in time of tails of solutions to the Boltzmann equation in the non-cutoff regime by examining the generation and propagation of $L^1$ and $L^\infty$ exponentially weighted estimates and the relation between them. For this purpose we introduce Mittag-Leffler moments which can be understood as a generalization of exponential moments. An interesting aspect of this result is that the singularity rate of the angular kernel affects the order of tails that can be shown to propagate in time. This is based on joint works with Alonso, Gamba, Pavlovic and Gamba, Pavlovic.<br />
<br />
<br />
===Ashish Kumar Pandey===<br />
<br />
Title: Instabilities in shallow water wave models<br />
<br />
Abstract: Slow modulations in wave characteristics of a nonlinear, periodic traveling wave in a dispersive medium may develop non-trivial structures which evolve as it propagates. This phenomenon is called modulational instability. In the context of water waves, this phenomenon was observed by Benjamin and Feir and, independently, by Whitham in Stokes' waves. I will discuss a general mechanism to study modulational instability of periodic traveling waves which can be applied to several classes of nonlinear dispersive equations including KdV, BBM, and regularized Boussinesq type equations.<br />
<br />
<br />
===Khai Nguyen===<br />
<br />
Title: Burgers Equation with Some Nonlocal Sources<br />
<br />
Abstract: Consider the Burgers equation with some nonlocal sources, which were derived from models of nonlinear wave with constant frequency. This talk will present some recent results on the global existence of entropy weak solutions, priori estimates, and a uniqueness result for both Burgers-Poisson and Burgers-Hilbert equations. Some open questions will be discussed.<br />
<br />
===Hongwei Gao=== <br />
<br />
Title: Stochastic homogenization of certain nonconvex Hamilton-Jacobi equations<br />
<br />
Abstract: In this talk, we discuss the stochastic homogenization of certain nonconvex Hamilton-Jacobi equations. The nonconvex Hamiltonians, which are generally uneven and inseparable, are generated by a sequence of (level-set) convex Hamiltonians and a sequence of (level-set) concave Hamiltonians through the min-max formula. We provide a monotonicity assumption on the contact values between those stably paired Hamiltonians so as to guarantee the stochastic homogenization. If time permits, we will talk about some homogenization results when the monotonicity assumption breaks down.<br />
<br />
===Huy Nguyen===<br />
<br />
Title : Compressible fluids and active potentials<br />
<br />
Abstract: We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion coefficients do not vanish, and give local and global existence results. The models include the barotropic compressible Navier-Stokes equations, shallow water systems and the lubrication approximation of slender jets. In all these models the momentum equation is forced by the gradient of a solution-dependent potential: the active potential. The method of proof uses the Bresch-Desjardins entropy and the analysis of the evolution of the active potential.<br />
<br />
===In-Jee Jeong===<br />
<br />
Title: Singularity formation for the 3D axisymmetric Euler equations<br />
<br />
Abstract: We consider the 3D axisymmetric Euler equations on exterior domains $\{ (x,y,z) : (1 + \epsilon|z|)^2 \le x^2 + y^2 \} $ for any $\epsilon > 0$ so that we can get arbitrarily close to the exterior of a cylinder. We construct a strong local well-posedness class, and show that within this class there exist compactly supported initial data which blows up in finite time. The local well-posedness class consists of velocities which are uniformly Lipschitz in space and have finite energy. Our results were inspired by recent works of Hou-Luo, Kiselev-Sverak, and many others, and the proof builds up on our previous works on 2D Euler and Boussinesq systems. This is joint work with Tarek Elgindi.<br />
<br />
===Jeff Calder===<br />
<br />
Title: Nonlinear PDE continuum limits in data science and machine learning<br />
<br />
Abstract: We will present some recent results on PDE continuum limits for (random) discrete problems in data science and machine learning. All of the problems satisfy a type of discrete comparison/maximum principle and so the continuum PDEs are properly interpreted in the viscosity sense. We will present results for nondominated sorting, convex hull peeling, and graph-based semi-supervised learning. Nondominated sorting is an algorithm for arranging points in Euclidean space into layers by repeatedly peeling away coordinatewise minimal points, and the continuum PDE turns out to be a Hamilton-Jacobi equation. Convex hull peeling is used to order data by repeatedly peeling the vertices of the convex hull, and the continuum limit is motion by a power of Gauss curvature. Finally, a recently proposed class of graph-based learning problems have PDE continuum limits corresponding to weighted p-Laplace equations. In each case the continuum PDEs provide insights into the data science/engineering problems, and suggest avenues for fast approximate algorithms based on the PDE interpretations.<br />
<br />
===Hitoshi Ishii===<br />
<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15428Colloquia2018-04-17T19:29:39Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
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!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13 (911 Van Vleck)<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#April 16, Christine Berkesch Zamaere (University of Minnesota)| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday, Room: 911)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Tsuda University) Wasow lecture<br />
|[[#April 25, Hitoshi Ishii (Tsuda University)| Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm, Room: B102 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm, Room: B325 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16, Christine Berkesch Zamaere (University of Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
<br />
===April 25, Hitoshi Ishii (Tsuda University)===<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Blank|Fall 2018]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15416Colloquia2018-04-15T20:57:28Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13 (911 Van Vleck)<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#April 16, Christine Berkesch Zamaere (University of Minnesota)| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Tsuda University) Wasow lecture<br />
|[[#April 25, Hitoshi Ishii (Tsuda University)| Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm, Room: B102 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm, Room: B325 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16, Christine Berkesch Zamaere (University of Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
<br />
===April 25, Hitoshi Ishii (Tsuda University)===<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Blank|Fall 2018]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15336Colloquia2018-04-04T21:31:38Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[# TBA| TBA ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15267Colloquia2018-03-16T19:42:27Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[# TBA| TBA ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15246Colloquia2018-03-13T20:48:04Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[# TBA| TBA ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 20<br />
| [http://www.math.stonybrook.edu/~xiu/ Xiuxiong Chen] (Stony Brook University, CANCELLED)<br />
|[[# Xiuxiong Chen| TBA ]]<br />
| Bing Wang<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15219Colloquia2018-03-09T15:52:14Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[# TBA| TBA ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 20<br />
| [http://www.math.stonybrook.edu/~xiu/ Xiuxiong Chen] (Stony Brook University)<br />
|[[# Xiuxiong Chen| TBA ]]<br />
| Bing Wang<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15218Colloquia2018-03-09T15:51:23Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[# TBA| TBA ]]<br />
| Erman and Sam<br />
|<br />
|-<br />
| April 20<br />
| [http://www.math.stonybrook.edu/~xiu/ Xiuxiong Chen] (Stony Brook University)<br />
|[[# Xiuxiong Chen| TBA ]]<br />
| Bing Wang<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15202Colloquia2018-03-01T20:24:00Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 20<br />
| Xiuxiong Chen(Stony Brook University)<br />
|[[# Xiuxiong Chen| TBA ]]<br />
| Bing Wang<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15031Colloquia2018-02-06T18:09:43Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[# TBA| TBA ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15030Colloquia2018-02-06T18:03:40Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[# TBA| TBA ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15029Colloquia2018-02-06T17:42:48Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| Aaron Bertram] (University of Utah)<br />
|[[# TBA| TBA ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=15028Colloquia2018-02-06T17:37:59Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14893Colloquia2018-01-29T16:25:50Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14892Colloquia2018-01-29T15:41:57Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14835Colloquia2018-01-24T16:11:35Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14833Colloquia2018-01-24T16:07:56Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#Li Chao| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Li Chao===<br />
<br />
January 29: Li Chao (Columbia)<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14795Colloquia2018-01-20T23:59:01Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 30<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<DATE>: <PERSON> (INSTITUTION)<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14793Colloquia2018-01-19T23:12:03Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 30<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<DATE>: <PERSON> (INSTITUTION)<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14792Colloquia2018-01-19T23:10:12Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 30<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
| February 9<br />
|Reserved<br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<DATE>: <PERSON> (INSTITUTION)<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=14435PDE Geometric Analysis seminar2017-10-24T20:33:14Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Spring 2018 | Tentative schedule for Spring 2018]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2017 ==<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|September 11<br />
|Mihaela Ifrim (UW)<br />
|[[#Mihaela Ifrim| Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation]]<br />
| Kim & Tran<br />
|- <br />
|September 18<br />
|Longjie Zhang (University of Tokyo) <br />
|[[#Longjie Zhang | On curvature flow with driving force starting as singular initial curve in the plane]]<br />
| Angenent<br />
|- <br />
|September 22,<br />
VV 9th floor hall, 4:00pm<br />
|Jaeyoung Byeon (KAIST) <br />
|[[#Jaeyoung Byeon| Colloquium: Patterns formation for elliptic systems with large interaction forces]]<br />
| Rabinowitz <br />
|- <br />
|September 25<br />
| Tuoc Phan (UTK)<br />
|[[#Tuoc Phan | Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application]]<br />
| Tran<br />
|- <br />
|September 26, <br />
VV B139 4:00pm<br />
| Hiroyoshi Mitake (Hiroshima University)<br />
|[[#Hiroyoshi Mitake | Joint Analysis/PDE seminar: Derivation of multi-layered interface system and its application]]<br />
| Tran<br />
|- <br />
|September 29,<br />
VV901 2:25pm<br />
| Dongnam Ko (CMU & SNU)<br />
|[[#Dongnam Ko | a joint seminar with ACMS: On the emergence of local flocking phenomena in Cucker-Smale ensembles ]]<br />
| Shi Jin & Kim<br />
|- <br />
|October 2<br />
| No seminar due to a KI-Net conference<br />
|<br />
|<br />
|- <br />
|October 9<br />
| Sameer Iyer (Brown University)<br />
|[[#Sameer Iyer | Global-in-x Steady Prandtl Expansion over a Moving Boundary ]]<br />
| Kim<br />
|- <br />
|October 16<br />
| Jingrui Cheng (UW)<br />
|[[#Jingrui Cheng | A 1-D semigeostrophic model with moist convection ]]<br />
| Kim & Tran<br />
|- <br />
|October 23<br />
| Donghyun Lee (UW)<br />
|[[#Donghyun Lee | The Vlasov-Poisson-Boltzmann system in bounded domains ]]<br />
| Kim & Tran<br />
|- <br />
|October 30<br />
| Myoungjean Bae (POSTECH)<br />
|[[#Myoungjean Bae | 3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system ]]<br />
| Feldman<br />
|- <br />
|November 6<br />
| Jingchen Hu (USTC and UW)<br />
|[[#Jingchen Hu | TBD ]]<br />
| Kim & Tran <br />
|- <br />
|December 4<br />
| Norbert Pozar (Kanazawa University)<br />
|[[#Norbert Pozar | TBD ]]<br />
| Tran<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Mihaela Ifrim===<br />
<br />
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation<br />
<br />
Our goal is to take a first step toward understanding the long time dynamics of solutions for the Benjamin-Ono equation. While this problem is known to be both completely integrable and globally well-posed in $L^2$, much less seems to be known concerning its long time dynamics. We present that for small localized data the solutions have (nearly) dispersive dynamics almost globally in time. An additional objective is to revisit the $L^2$ theory for the Benjamin-Ono equation and provide a simpler, self-contained approach. This is joined work with Daniel Tataru.<br />
<br />
===Longjie Zhang===<br />
<br />
On curvature flow with driving force starting as singular initial curve in the plane<br />
<br />
We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the plane. However, the initial curve is oriented singularly at origin. We investigate this problem by level set method and give some criteria to judge whether the interface evolution is fattening or not. In the end, we can classify the solutions into three categories and provide the asymptotic behavior in each category. Our main tools in this paper are level set method and intersection number principle.<br />
<br />
===Jaeyoung Byeon===<br />
<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
<br />
===Tuoc Phan===<br />
Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application.<br />
<br />
Abstract: In this talk, we first introduce a problem on the existence of global time smooth solutions for a system of cross-diffusion equations. We then recall some classical results on regularity theories, and show that to solve our problem, new results on regularity theory estimates of Calderon-Zygmund type for gradients of solutions to a class of parabolic equations in Lebesgue spaces are required. We then discuss a result on Calderon-Zygmnud type estimate in the concrete setting to solve our<br />
mentioned problem regarding the system of cross-diffusion equations. The remaining part of the talk will be focused on some new generalized results on regularity gradient estimates for some general class of quasi-linear parabolic equations. Regularity estimates for gradients of solutions in Lorentz spaces will be presented. Ideas of the proofs for the results are given.<br />
<br />
===Hiroyoshi Mitake===<br />
Derivation of multi-layered interface system and its application<br />
<br />
Abstract: In this talk, I will propose a multi-layered interface system which can be formally derived by the singular limit of the weakly coupled system of the Allen-Cahn equation. By using the level set approach, this system can be written as a quasi-monotone degenerate parabolic system. We give results of the well-posedness of viscosity solutions, and study the singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.<br />
<br />
<br />
===Dongnam Ko===<br />
On the emergence of local flocking phenomena in Cucker-Smale ensembles<br />
<br />
Emergence of flocking groups are often observed in many complex network systems. The Cucker-Smale model is one of the flocking model, which describes the dynamics of attracting particles. This talk concerns time-asymptotic behaviors of Cucker-Smale particle ensembles, especially for mono-cluster and bi-cluster flockings. The emergence of flocking phenomena is determined by sufficient initial conditions, coupling strength, and communication weight decay. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system. We derive a system of differential inequalities for the functionals that measure the local fluctuations and group separations along particle trajectories. The bootstrapping argument is the key idea to prove the gathering and separating behaviors of Cucker-Smale particles simultaneously.<br />
<br />
===Sameer Iyer===<br />
Title: Global-in-x Steady Prandtl Expansion over a Moving Boundary.<br />
<br />
Abstract: I will outline the proof that steady, incompressible Navier-Stokes flows posed over the moving boundary, y = 0, can be decomposed into Euler and Prandtl flows globally in the tangential variable, assuming a sufficiently small velocity mismatch. The main obstacles in the analysis center around obtaining sharp decay rates for the linearized profiles and the remainders. The remainders are controlled via a high-order energy method, supplemented with appropriate embedding theorems, which I will present.<br />
<br />
===Jingrui Cheng===<br />
<br />
A 1-D semigeostrophic model with moist convection.<br />
<br />
We consider a simplified 1-D model of semigeostrophic system with moisture, which describes moist convection in a single column in the atmosphere. In general, the solution is non-continuous and it is nontrivial part of the problem to find a suitable definition of weak solutions. We propose a plausible definition of such weak solutions which describes the evolution of the probability distribution of the physical quantities, so that the equations hold in the sense of almost everywhere. Such solutions are constructed from a discrete scheme which obeys the physical principles. This is joint work with Mike Cullen, together with Bin Cheng, John Norbury and Matthew Turner.<br />
<br />
===Donghyun Lee===<br />
<br />
We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition. Moreover we prove an exponential convergence of distribution function toward the global Maxwellian.<br />
<br />
===Myoungjean Bae===<br />
<br />
3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system.<br />
<br />
I will present a recent result on the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler–Poisson system in a cylinder supplemented with non-small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl (=angular momentum density) component. This talk is based on a joint work with S. Weng (Wuhan University, China).</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=14076PDE Geometric Analysis seminar2017-09-06T21:19:12Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Spring 2018 | Tentative schedule for Spring 2018]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2017 ==<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|September 11<br />
| Mihaela Ifrim (UW)<br />
|[[Mihaela Ifrim | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|September 18<br />
| Longjie Zhang (University of Tokyo) <br />
|[[Longjie Zhang | TBD ]]<br />
| Angenent<br />
|- <br />
|September 22,<br />
VV B239 4:00pm<br />
| Jaeyoung Byeon (KAIST) <br />
|[[Jaeyoung Byeon| Colloquium: Patterns formation for elliptic systems with large interaction forces]]<br />
| Rabinowitz <br />
|- <br />
|September 25<br />
| Tuoc Phan (UTK)<br />
|[[Tuoc Phan | TBD ]]<br />
| Tran<br />
|- <br />
|September 26, <br />
VV B139 4:00pm<br />
| Hiroyoshi Mitake (Hiroshima University)<br />
|[[Hiroyoshi Mitake | Joint Analysis/PDE seminar ]]<br />
| Tran<br />
|- <br />
|September 29,<br />
VV901 2:25pm<br />
| Dongnam Ko (CMU & SNU)<br />
|[[Dongnam Ko | a joint seminar with ACMS: TBD ]]<br />
| Shi Jin & Kim<br />
|- <br />
|October 2<br />
| No seminar due to a KI-Net conference<br />
|<br />
|<br />
|- <br />
|October 9<br />
| Sameer Iyer (Brown University)<br />
|[[Sameer Iyer | TBD ]]<br />
| Kim<br />
|- <br />
|October 16<br />
| Jingrui Cheng (UW)<br />
|[[Jingrui Cheng | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|October 23<br />
| Donghyun Lee (UW)<br />
|[[Donghyun Lee | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|October 30<br />
| Myoungjean Bae (POSTECH)<br />
|[[ Myoungjean Bae | TBD ]]<br />
| Feldman<br />
|- <br />
|November 6<br />
| Jingchen Hu (USTC and UW)<br />
|[[Jingchen Hu | TBD ]]<br />
| Kim & Tran<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Mihaela Ifrim===<br />
<br />
===Jaeyoung Byeon===<br />
<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=14063Colloquia2017-09-05T18:54:08Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|November 3<br />
|Alexander Yom Din (Caltech)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13984Colloquia2017-08-28T16:45:15Z<p>Feldman: /* Mathematics Colloquium */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
| TBA<br />
|[[# TBA| TBA ]]<br />
| Spagnolie<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byeon (KAIST)<br />
|[[# TBA| TBA ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|November 3<br />
|Alexander Yom Din (Caltech)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13983Colloquia2017-08-28T16:44:17Z<p>Feldman: /* Mathematics Colloquium */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Spagnolie<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byeon (KAIST)<br />
|[[# TBA| TBA ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|November 3<br />
|Alexander Yom Din (Caltech)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13884Colloquia2017-08-07T14:21:43Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byeon (KAIST)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13883Colloquia2017-08-07T14:06:55Z<p>Feldman: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byun (KAIST)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13716Colloquia2017-04-28T20:38:43Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[#Schenck | Hyperplane Arrangements: Algebra, Combinatorics, Topology ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14, B239<br />
| [http://www.math.ucla.edu/~wgangbo/ Wilfrid Gangbo] (UCLA)<br />
|[[#Friday, April 14: Wilfrid Gangbo (UCLA) | On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math> ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 17, B239<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Monday, April 17: Ravi Vakil (Stanford) | The Mathematics of Doodling (Public Lecture) ]]<br />
|Erman<br />
|<br />
|-<br />
|April 18, 9th floor<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Tuesday, April 18: Ravi Vakil (Stanford) | Cutting and Pasting in Algebraic Geometry ]]<br />
|Erman<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[#Friday, April 28: Thomas Yizhao Hou (Caltech) | The interplay between theory and computation in the study of 3D Euler equations]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
<br />
=== Friday, April 7: Hal Schenck (UIUC) ===<br />
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''<br />
<br />
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. <br />
The complement X of the hypersurfaces has<br />
very interesting topology. In 1980 Orlik and Solomon determined<br />
that the cohomology ring is a quotient of an<br />
exterior algebra, with a generator for each hyperplane.<br />
Surprisingly, all relations are determined by the combinatorics<br />
of the arrangement. Nevertheless, there remain many interesting<br />
open questions, which involve a beautiful interplay of algebra,<br />
combinatorics, geometry, and topology. I'll spend much of the<br />
talk discussing this interplay, and close by discussing several<br />
conjectures in the field, along with recent progress on those<br />
conjectures, where the Bernstein-Gelfand-Gelfand correspondence<br />
plays a key role. Joint work with Dan Cohen (LSU) and Alex<br />
Suciu (Northeastern).<br />
<br />
<br />
=== Friday, April 14: Wilfrid Gangbo (UCLA) ===<br />
''On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math>''<br />
<br />
We elucidate the connection between different notions of differentiability in <math>P_2(R^d) </math>: some have been introduced intrinsically by Ambrosio-Gigli-Savare, the other notion due to Lions, is extrinsic and arises from the identification of <math> P_2(R^d) </math> with the Hilbert space of square-integrable random variables. We mention potential applications such as uniqueness of viscosity solutions for Hamilton-Jacobi equations in <math> P_2(R^d) </math>, the latter not known to satisfy the Radon–Nikodym property. (This talk is based on a work in progress with A Tudorascu).<br />
<br />
<br />
=== Monday, April 17: Ravi Vakil (Stanford) ===<br />
''The Mathematics of Doodling''<br />
<br />
Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.<br />
<br />
<br />
=== Tuesday, April 18: Ravi Vakil (Stanford) ===<br />
''Cutting and pasting in (algebraic) geometry''<br />
<br />
Given some class of "geometric space", we can make a ring as follows.<br />
<br />
<b> Additive Structure:</b> When U is an open subset of X we set [X] = [U] + [U \ X].<br />
<br />
<b> Multiplicative Structure:</b> [X x Y] = [X][Y]<br />
<br />
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology. I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural). A motivating example will be polynomials in one variable. This talk is intended for a broad audience. This is joint work with Melanie Matchett Wood.<br />
<br />
<br />
=== Friday, April 28: Thomas Yizhao Hou (Caltech) ===<br />
''The interplay between theory and computation in the study of 3D Euler equations''<br />
<br />
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities. To resolve the nearly singular solution, we develop specially designed adaptive (moving) meshes with a maximum effective resolution of order $10^12$ in each direction. A careful local analysis also suggests that the blowing-up solution is highly anisotropic and is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. Very recently we prove rigorously that the 1D model develops finite time singularity. Using a very delicate method of analysis which involves computer assisted proof, we prove the existence of a discrete family of self-similar profiles for a variant of this model. Moreover, we show that the self-similar profile enjoys some stability property.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13715Colloquia2017-04-28T20:32:55Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[#Schenck | Hyperplane Arrangements: Algebra, Combinatorics, Topology ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14, B239<br />
| [http://www.math.ucla.edu/~wgangbo/ Wilfrid Gangbo] (UCLA)<br />
|[[#Friday, April 14: Wilfrid Gangbo (UCLA) | On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math> ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 17, B239<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Monday, April 17: Ravi Vakil (Stanford) | The Mathematics of Doodling (Public Lecture) ]]<br />
|Erman<br />
|<br />
|-<br />
|April 18, 9th floor<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Tuesday, April 18: Ravi Vakil (Stanford) | Cutting and Pasting in Algebraic Geometry ]]<br />
|Erman<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[#Friday, April 28: Thomas Yizhao Hou (Caltech) | The interplay between theory and computation in the study of 3D Euler equations]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|Jonathan Hauenstein<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
<br />
=== Friday, April 7: Hal Schenck (UIUC) ===<br />
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''<br />
<br />
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. <br />
The complement X of the hypersurfaces has<br />
very interesting topology. In 1980 Orlik and Solomon determined<br />
that the cohomology ring is a quotient of an<br />
exterior algebra, with a generator for each hyperplane.<br />
Surprisingly, all relations are determined by the combinatorics<br />
of the arrangement. Nevertheless, there remain many interesting<br />
open questions, which involve a beautiful interplay of algebra,<br />
combinatorics, geometry, and topology. I'll spend much of the<br />
talk discussing this interplay, and close by discussing several<br />
conjectures in the field, along with recent progress on those<br />
conjectures, where the Bernstein-Gelfand-Gelfand correspondence<br />
plays a key role. Joint work with Dan Cohen (LSU) and Alex<br />
Suciu (Northeastern).<br />
<br />
<br />
=== Friday, April 14: Wilfrid Gangbo (UCLA) ===<br />
''On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math>''<br />
<br />
We elucidate the connection between different notions of differentiability in <math>P_2(R^d) </math>: some have been introduced intrinsically by Ambrosio-Gigli-Savare, the other notion due to Lions, is extrinsic and arises from the identification of <math> P_2(R^d) </math> with the Hilbert space of square-integrable random variables. We mention potential applications such as uniqueness of viscosity solutions for Hamilton-Jacobi equations in <math> P_2(R^d) </math>, the latter not known to satisfy the Radon–Nikodym property. (This talk is based on a work in progress with A Tudorascu).<br />
<br />
<br />
=== Monday, April 17: Ravi Vakil (Stanford) ===<br />
''The Mathematics of Doodling''<br />
<br />
Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.<br />
<br />
<br />
=== Tuesday, April 18: Ravi Vakil (Stanford) ===<br />
''Cutting and pasting in (algebraic) geometry''<br />
<br />
Given some class of "geometric space", we can make a ring as follows.<br />
<br />
<b> Additive Structure:</b> When U is an open subset of X we set [X] = [U] + [U \ X].<br />
<br />
<b> Multiplicative Structure:</b> [X x Y] = [X][Y]<br />
<br />
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology. I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural). A motivating example will be polynomials in one variable. This talk is intended for a broad audience. This is joint work with Melanie Matchett Wood.<br />
<br />
<br />
=== Friday, April 28: Thomas Yizhao Hou (Caltech) ===<br />
''The interplay between theory and computation in the study of 3D Euler equations''<br />
<br />
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities. To resolve the nearly singular solution, we develop specially designed adaptive (moving) meshes with a maximum effective resolution of order $10^12$ in each direction. A careful local analysis also suggests that the blowing-up solution is highly anisotropic and is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. Very recently we prove rigorously that the 1D model develops finite time singularity. Using a very delicate method of analysis which involves computer assisted proof, we prove the existence of a discrete family of self-similar profiles for a variant of this model. Moreover, we show that the self-similar profile enjoys some stability property.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13714Colloquia2017-04-28T15:56:19Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[#Schenck | Hyperplane Arrangements: Algebra, Combinatorics, Topology ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14, B239<br />
| [http://www.math.ucla.edu/~wgangbo/ Wilfrid Gangbo] (UCLA)<br />
|[[#Friday, April 14: Wilfrid Gangbo (UCLA) | On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math> ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 17, B239<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Monday, April 17: Ravi Vakil (Stanford) | The Mathematics of Doodling (Public Lecture) ]]<br />
|Erman<br />
|<br />
|-<br />
|April 18, 9th floor<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Tuesday, April 18: Ravi Vakil (Stanford) | Cutting and Pasting in Algebraic Geometry ]]<br />
|Erman<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[#Friday, April 28: Thomas Yizhao Hou (Caltech) | The interplay between theory and computation in the study of 3D Euler equations]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|Jonathan Hauenstein<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
<br />
=== Friday, April 7: Hal Schenck (UIUC) ===<br />
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''<br />
<br />
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. <br />
The complement X of the hypersurfaces has<br />
very interesting topology. In 1980 Orlik and Solomon determined<br />
that the cohomology ring is a quotient of an<br />
exterior algebra, with a generator for each hyperplane.<br />
Surprisingly, all relations are determined by the combinatorics<br />
of the arrangement. Nevertheless, there remain many interesting<br />
open questions, which involve a beautiful interplay of algebra,<br />
combinatorics, geometry, and topology. I'll spend much of the<br />
talk discussing this interplay, and close by discussing several<br />
conjectures in the field, along with recent progress on those<br />
conjectures, where the Bernstein-Gelfand-Gelfand correspondence<br />
plays a key role. Joint work with Dan Cohen (LSU) and Alex<br />
Suciu (Northeastern).<br />
<br />
<br />
=== Friday, April 14: Wilfrid Gangbo (UCLA) ===<br />
''On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math>''<br />
<br />
We elucidate the connection between different notions of differentiability in <math>P_2(R^d) </math>: some have been introduced intrinsically by Ambrosio-Gigli-Savare, the other notion due to Lions, is extrinsic and arises from the identification of <math> P_2(R^d) </math> with the Hilbert space of square-integrable random variables. We mention potential applications such as uniqueness of viscosity solutions for Hamilton-Jacobi equations in <math> P_2(R^d) </math>, the latter not known to satisfy the Radon–Nikodym property. (This talk is based on a work in progress with A Tudorascu).<br />
<br />
<br />
=== Monday, April 17: Ravi Vakil (Stanford) ===<br />
''The Mathematics of Doodling''<br />
<br />
Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.<br />
<br />
<br />
=== Tuesday, April 18: Ravi Vakil (Stanford) ===<br />
''Cutting and pasting in (algebraic) geometry''<br />
<br />
Given some class of "geometric space", we can make a ring as follows.<br />
<br />
<b> Additive Structure:</b> When U is an open subset of X we set [X] = [U] + [U \ X].<br />
<br />
<b> Multiplicative Structure:</b> [X x Y] = [X][Y]<br />
<br />
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology. I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural). A motivating example will be polynomials in one variable. This talk is intended for a broad audience. This is joint work with Melanie Matchett Wood.<br />
<br />
<br />
=== Friday, April 28: Thomas Yizhao Hou (Caltech) ===<br />
''The interplay between theory and computation in the study of 3D Euler equations''<br />
<br />
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities. To resolve the nearly singular solution, we develop specially designed adaptive (moving) meshes with a maximum effective resolution of order $10^12$ in each direction. A careful local analysis also suggests that the blowing-up solution is highly anisotropic and is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. Very recently we prove rigorously that the 1D model develops finite time singularity. Using a very delicate method of analysis which involves computer assisted proof, we prove the existence of a discrete family of self-similar profiles for a variant of this model. Moreover, we show that the self-similar profile enjoys some stability property.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13661Colloquia2017-04-13T22:46:45Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[#Schenck | Hyperplane Arrangements: Algebra, Combinatorics, Topology ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14, B239<br />
| [http://www.math.ucla.edu/~wgangbo/ Wilfrid Gangbo] (UCLA)<br />
|[[#Friday, April 14: Wilfrid Gangbo (UCLA) | On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math> ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 17, B239<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Monday, April 17: Ravi Vakil (Stanford) | The Mathematics of Doodling (Public Lecture) ]]<br />
|Erman<br />
|<br />
|-<br />
|April 18, 9th floor<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil] (Stanford)<br />
|[[#Tuesday, April 18: Ravi Vakil (Stanford) | Cutting and Pasting in Algebraic Geometry ]]<br />
|Erman<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
<br />
=== Friday, April 7: Hal Schenck (UIUC) ===<br />
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''<br />
<br />
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. <br />
The complement X of the hypersurfaces has<br />
very interesting topology. In 1980 Orlik and Solomon determined<br />
that the cohomology ring is a quotient of an<br />
exterior algebra, with a generator for each hyperplane.<br />
Surprisingly, all relations are determined by the combinatorics<br />
of the arrangement. Nevertheless, there remain many interesting<br />
open questions, which involve a beautiful interplay of algebra,<br />
combinatorics, geometry, and topology. I'll spend much of the<br />
talk discussing this interplay, and close by discussing several<br />
conjectures in the field, along with recent progress on those<br />
conjectures, where the Bernstein-Gelfand-Gelfand correspondence<br />
plays a key role. Joint work with Dan Cohen (LSU) and Alex<br />
Suciu (Northeastern).<br />
<br />
<br />
=== Friday, April 14: Wilfrid Gangbo (UCLA) ===<br />
''On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math>''<br />
<br />
We elucidate the connection between different notions of differentiability in <math>P_2(R^d) </math>: some have been introduced intrinsically by Ambrosio-Gigli-Savare, the other notion due to Lions, is extrinsic and arises from the identification of <math> P_2(R^d) </math> with the Hilbert space of square-integrable random variables. We mention potential applications such as uniqueness of viscosity solutions for Hamilton-Jacobi equations in <math> P_2(R^d) </math>, the latter not known to satisfy the Radon–Nikodym property. (This talk is based on a work in progress with A Tudorascu).<br />
<br />
<br />
=== Monday, April 17: Ravi Vakil (Stanford) ===<br />
''The Mathematics of Doodling''<br />
<br />
Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.<br />
<br />
<br />
=== Tuesday, April 18: Ravi Vakil (Stanford) ===<br />
''Cutting and pasting in (algebraic) geometry''<br />
<br />
Given some class of "geometric space", we can make a ring as follows.<br />
<br />
<b> Additive Structure:</b> When U is an open subset of X we set [X] = [U] + [U \ X].<br />
<br />
<b> Multiplicative Structure:</b> [X x Y] = [X][Y]<br />
<br />
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology. I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural). A motivating example will be polynomials in one variable. This talk is intended for a broad audience. This is joint work with Melanie Matchett Wood.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13660Colloquia2017-04-13T22:18:21Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[#Schenck | Hyperplane Arrangements: Algebra, Combinatorics, Topology ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14, B239<br />
| [http://www.math.ucla.edu/~wgangbo/ Wilfrid Gangbo] (UCLA)<br />
|[[#Friday, April 14: Wilfrid Gangbo (UCLA) | On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math> ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 17<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil]<br />
|[[#Doodling | The Mathematics of Doodling (Public Lecture) ]]<br />
|Erman<br />
|<br />
|-<br />
|April 18<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil]<br />
|[[#CutPaste | Cutting and Pasting in Algebraic Geometry ]]<br />
|Erman<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
<br />
=== Friday, April 7: Hal Schenck (UIUC) ===<br />
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''<br />
<br />
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. <br />
The complement X of the hypersurfaces has<br />
very interesting topology. In 1980 Orlik and Solomon determined<br />
that the cohomology ring is a quotient of an<br />
exterior algebra, with a generator for each hyperplane.<br />
Surprisingly, all relations are determined by the combinatorics<br />
of the arrangement. Nevertheless, there remain many interesting<br />
open questions, which involve a beautiful interplay of algebra,<br />
combinatorics, geometry, and topology. I'll spend much of the<br />
talk discussing this interplay, and close by discussing several<br />
conjectures in the field, along with recent progress on those<br />
conjectures, where the Bernstein-Gelfand-Gelfand correspondence<br />
plays a key role. Joint work with Dan Cohen (LSU) and Alex<br />
Suciu (Northeastern).<br />
<br />
<br />
=== Friday, April 14: Wilfrid Gangbo (UCLA) ===<br />
''On intrinsic differentiability in the Wasserstein space <math> P_2(R^d) </math>''<br />
<br />
We elucidate the connection between different notions of differentiability in <math>P_2(R^d) </math>: some have been introduced intrinsically by Ambrosio-Gigli-Savare, the other notion due to Lions, is extrinsic and arises from the identification of <math> P_2(R^d) </math> with the Hilbert space of square-integrable random variables. We mention potential applications such as uniqueness of viscosity solutions for Hamilton-Jacobi equations in <math> P_2(R^d) </math>, the latter not known to satisfy the Radon–Nikodym property. (This talk is based on a work in progress with A Tudorascu).<br />
<br />
<br />
=== Monday, April 17: Ravi Vakil (Stanford) ===<br />
''The Mathematics of Doodling''<br />
<br />
Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.<br />
<br />
<br />
=== Tuesday, April 18: Ravi Vakil (Stanford) ===<br />
''Cutting and pasting in (algebraic) geometry''<br />
<br />
Given some class of "geometric space", we can make a ring as follows.<br />
<br />
<b> Additive Structure:</b> When U is an open subset of X we set [X] = [U] + [U \ X].<br />
<br />
<b> Multiplicative Structure:</b> [X x Y] = [X][Y]<br />
<br />
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology. I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural). A motivating example will be polynomials in one variable. This talk is intended for a broad audience. This is joint work with Melanie Matchett Wood.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13610Colloquia2017-04-03T20:06:29Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[#Schenck | Hyperplane Arrangements: Algebra, Combinatorics, Topology ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 17<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil]<br />
|[[#Doodling | The Mathematics of Doodling (Public Lecture) ]]<br />
|Erman<br />
|<br />
|-<br />
|April 18<br />
| [http://math.stanford.edu/~vakil/ Ravi Vakil]<br />
|[[#CutPaste | Cutting and Pasting in Algebraic Geometry ]]<br />
|Erman<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
<br />
=== Friday, April 7: Hal Schenck (UIUC) ===<br />
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''<br />
<br />
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. <br />
The complement X of the hypersurfaces has<br />
very interesting topology. In 1980 Orlik and Solomon determined<br />
that the cohomology ring is a quotient of an<br />
exterior algebra, with a generator for each hyperplane.<br />
Surprisingly, all relations are determined by the combinatorics<br />
of the arrangement. Nevertheless, there remain many interesting<br />
open questions, which involve a beautiful interplay of algebra,<br />
combinatorics, geometry, and topology. I'll spend much of the<br />
talk discussing this interplay, and close by discussing several<br />
conjectures in the field, along with recent progress on those<br />
conjectures, where the Bernstein-Gelfand-Gelfand correspondence<br />
plays a key role. Joint work with Dan Cohen (LSU) and Alex<br />
Suciu (Northeastern).<br />
<br />
<br />
=== Monday, April 17: Ravi Vakil (Stanford) ===<br />
''The Mathematics of Doodling''<br />
<br />
Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.<br />
<br />
<br />
=== Tuesday, April 18: Ravi Vakil (Stanford) ===<br />
''Cutting and pasting in (algebraic) geometry''<br />
<br />
Given some class of "geometric space", we can make a ring as follows.<br />
<br />
<b> Additive Structure:</b> When U is an open subset of X we set [X] = [U] + [U \ X].<br />
<br />
<b> Multiplicative Structure:</b> [X x Y] = [X][Y]<br />
<br />
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology. I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural). A motivating example will be polynomials in one variable. This talk is intended for a broad audience. This is joint work with Melanie Matchett Wood.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13560PDE Geometric Analysis seminar2017-03-27T15:55:12Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2016 | Tentative schedule for Fall 2017]]===<br />
<br />
= PDE GA Seminar Schedule Spring 2017 =<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|-<br />
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck<br />
| Sigurd Angenent (UW)<br />
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]<br />
| Kim & Tran<br />
|- <br />
<br />
<br />
|-<br />
|February 6 - Wasow lecture<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Jin<br />
|- <br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[#Bing Wang | The extension problem of the mean curvature flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 20<br />
| Eric Baer (UW)<br />
|[[#Eric Baer | Isoperimetric sets inside almost-convex cones]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | Homogenization of pathwise Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]<br />
| Smith <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Analysis/Applied math/PDE seminar<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]<br />
| Smith<br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | Global $L^p$ well posed-ness of the Boltzmann equation with an angle-potential concentrated collision kernel.]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Mean-Field Limits for Ginzburg-Landau vortices ]]<br />
| Tran<br />
<br />
|-<br />
|March 29 - Wasow lecture<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Microscopic description of Coulomb-type systems ]]<br />
| <br />
<br />
<br />
|-<br />
|March 30 <br>Special day (Thursday) and location:<br> B139 Van Vleck<br />
| Gui-Qiang Chen (Oxford)<br />
|[[#Gui-Qiang Chen | Supersonic Flow onto Solid Wedges,<br />
Multidimensional Shock Waves and Free Boundary Problems ]]<br />
| Feldman<br />
<br />
<br />
<br />
|-<br />
|April 3<br />
| Zhenfu Wang (Maryland)<br />
|[[#Zhenfu Wang | ]]<br />
| Kim<br />
<br />
|-<br />
|April 10<br />
| Andrei Tarfulea (Chicago)<br />
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]<br />
| Baer<br />
<br />
|-<br />
|April 17<br />
| Siao-Hao Guo (Rutgers)<br />
|[[# Siao-Hao Guo | Analysis of Velázquez's solution to the mean curvature flow with a type II singularity]]<br />
| Lu Wang<br />
<br />
<br />
|-<br />
|April 24<br />
| Jianfeng Lu<br />
|[[#Jianfeng Lu | TBA]]<br />
| Li<br />
<br />
|-<br />
|April 25- joint Analysis/PDE seminar<br />
| Chris Henderson (Chicago)<br />
|[[#Chris Henderson | TBA]]<br />
| Lin<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Sigurd Angenent===<br />
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo; In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.<br />
<br />
===Serguei Denissov===<br />
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.<br />
<br />
<br />
===Bing Wang===<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.<br />
<br />
===Eric Baer===<br />
We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones. Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere. The work we describe is joint with A. Figalli.<br />
<br />
===Ben Seeger===<br />
I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.<br />
<br />
===Sona Akopian===<br />
Global $L^p$ well posed-ness of the Boltzmann equation with an angle-potential concentrated collision kernel.<br />
<br />
We solve the Cauchy problem associated to an epsilon-parameter family of homogeneous Boltzmann equations for very soft and Coulomb potentials. Proposed in 2013 by Bobylev and Potapenko, the collision kernel that we use is a Dirac mass concentrated at very small angles and relative speeds. The main advantage of such a kernel is that it does not separate its variables (relative speed $u$ and scattering angle $\theta$) and can be viewed as a pseudo-Maxwell molecule collision kernel, which allows for the splitting of the Boltzmann collision operator into its gain and loss terms. Global estimates on the gain term gives us an existence theory for $L^1_k \capL^p$ with any $k\geq 2$ and $p\geq 1.$ Furthermore the bounds we obtain are independent of the epsilon parameter, which allows for analysis of the solutions in the grazing collisions limit, i.e., when epsilon approaches zero and the Boltzmann equation becomes the Landau equation. <br />
<br />
===Sylvia Serfaty===<br />
Mean-Field Limits for Ginzburg-Landau vortices<br />
<br />
Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.<br />
<br />
<br />
===Gui-Qiang Chen===<br />
Supersonic Flow onto Solid Wedges, Multidimensional Shock Waves and Free Boundary Problems<br />
<br />
When an upstream steady uniform supersonic flow, governed by the Euler equations,<br />
impinges onto a symmetric straight-sided wedge, there are two possible steady oblique shock<br />
configurations if the wedge angle is less than the detachment angle -- the steady weak shock<br />
with supersonic or subsonic downstream flow (determined by the wedge angle that is less or larger<br />
than the sonic angle) and the steady strong shock with subsonic downstream flow, both of which<br />
satisfy the entropy conditions.<br />
The fundamental issue -- whether one or both of the steady weak and strong shocks are physically<br />
admissible solutions -- has been vigorously debated over the past eight decades.<br />
In this talk, we discuss some of the most recent developments on the stability analysis<br />
of the steady shock solutions in both the steady and dynamic regimes.<br />
The corresponding stability problems can be formulated as free boundary problems<br />
for nonlinear partial differential equations of mixed elliptic-hyperbolic type, whose<br />
solutions are fundamental for multidimensional hyperbolic conservation laws.<br />
Some further developments, open problems, and mathematical challenges in this direction<br />
are also addressed.<br />
<br />
===Andrei Tarfulea===<br />
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and<br />
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.<br />
<br />
===Siao-hao Guo===<br />
Analysis of Velázquez's solution to the mean curvature flow with a type II singularity<br />
<br />
Velázquez discovered a solution to the mean curvature flow which develops a type II singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution, the rescaled flow converges in the C^0 sense to a minimal hypersurface which is tangent to Simons' cone at infinity. In this talk, we will present that the rescaled flow actually converges locally smoothly to the minimal hypersurface, which appears to be the singularity model of the type II singularity. In addition, we will show that the mean curvature of the solution blows up near the origin at a rate which is smaller than that of the second fundamental form. This is a joint work with N. Sesum.</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13554PDE Geometric Analysis seminar2017-03-24T21:35:31Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2016 | Tentative schedule for Fall 2017]]===<br />
<br />
= PDE GA Seminar Schedule Spring 2017 =<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|-<br />
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck<br />
| Sigurd Angenent (UW)<br />
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]<br />
| Kim & Tran<br />
|- <br />
<br />
<br />
|-<br />
|February 6 - Wasow lecture<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Jin<br />
|- <br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[#Bing Wang | The extension problem of the mean curvature flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 20<br />
| Eric Baer (UW)<br />
|[[#Eric Baer | Isoperimetric sets inside almost-convex cones]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | Homogenization of pathwise Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]<br />
| Smith <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Analysis/Applied math/PDE seminar<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]<br />
| Smith<br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | Global $L^p$ well posed-ness of the Boltzmann equation with an angle-potential concentrated collision kernel.]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Mean-Field Limits for Ginzburg-Landau vortices ]]<br />
| Tran<br />
<br />
|-<br />
|March 29 - Wasow lecture<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Microscopic description of Coulomb-type systems ]]<br />
| <br />
<br />
<br />
|-<br />
|March 30 - special seminar<br />
| Gui-Qiang Chen (Oxford)<br />
|[[#Gui-Qiang Chen | Supersonic Flow onto Solid Wedges,<br />
Multidimensional Shock Waves and Free Boundary Problems ]]<br />
| Feldman<br />
<br />
<br />
<br />
|-<br />
|April 3<br />
| Zhenfu Wang (Maryland)<br />
|[[#Zhenfu Wang | ]]<br />
| Kim<br />
<br />
|-<br />
|April 10<br />
| Andrei Tarfulea (Chicago)<br />
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]<br />
| Baer<br />
<br />
|-<br />
|April 17<br />
| Siao-Hao Guo (Rutgers)<br />
|[[# Siao-Hao Guo | Analysis of Velázquez's solution to the mean curvature flow with a type II singularity]]<br />
| Lu Wang<br />
<br />
<br />
|-<br />
|April 24<br />
| Jianfeng Lu<br />
|[[#Jianfeng Lu | TBA]]<br />
| Li<br />
<br />
|-<br />
|April 25- joint Analysis/PDE seminar<br />
| Chris Henderson (Chicago)<br />
|[[#Chris Henderson | TBA]]<br />
| Lin<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Sigurd Angenent===<br />
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo; In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.<br />
<br />
===Serguei Denissov===<br />
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.<br />
<br />
<br />
===Bing Wang===<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.<br />
<br />
===Eric Baer===<br />
We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones. Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere. The work we describe is joint with A. Figalli.<br />
<br />
===Ben Seeger===<br />
I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.<br />
<br />
===Sona Akopian===<br />
Global $L^p$ well posed-ness of the Boltzmann equation with an angle-potential concentrated collision kernel.<br />
<br />
We solve the Cauchy problem associated to an epsilon-parameter family of homogeneous Boltzmann equations for very soft and Coulomb potentials. Proposed in 2013 by Bobylev and Potapenko, the collision kernel that we use is a Dirac mass concentrated at very small angles and relative speeds. The main advantage of such a kernel is that it does not separate its variables (relative speed $u$ and scattering angle $\theta$) and can be viewed as a pseudo-Maxwell molecule collision kernel, which allows for the splitting of the Boltzmann collision operator into its gain and loss terms. Global estimates on the gain term gives us an existence theory for $L^1_k \capL^p$ with any $k\geq 2$ and $p\geq 1.$ Furthermore the bounds we obtain are independent of the epsilon parameter, which allows for analysis of the solutions in the grazing collisions limit, i.e., when epsilon approaches zero and the Boltzmann equation becomes the Landau equation. <br />
<br />
===Sylvia Serfaty===<br />
Mean-Field Limits for Ginzburg-Landau vortices<br />
<br />
Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.<br />
<br />
<br />
===Gui-Qiang Chen===<br />
Supersonic Flow onto Solid Wedges, Multidimensional Shock Waves and Free Boundary Problems<br />
<br />
When an upstream steady uniform supersonic flow, governed by the Euler equations,<br />
impinges onto a symmetric straight-sided wedge, there are two possible steady oblique shock<br />
configurations if the wedge angle is less than the detachment angle -- the steady weak shock<br />
with supersonic or subsonic downstream flow (determined by the wedge angle that is less or larger<br />
than the sonic angle) and the steady strong shock with subsonic downstream flow, both of which<br />
satisfy the entropy conditions.<br />
The fundamental issue -- whether one or both of the steady weak and strong shocks are physically<br />
admissible solutions -- has been vigorously debated over the past eight decades.<br />
In this talk, we discuss some of the most recent developments on the stability analysis<br />
of the steady shock solutions in both the steady and dynamic regimes.<br />
The corresponding stability problems can be formulated as free boundary problems<br />
for nonlinear partial differential equations of mixed elliptic-hyperbolic type, whose<br />
solutions are fundamental for multidimensional hyperbolic conservation laws.<br />
Some further developments, open problems, and mathematical challenges in this direction<br />
are also addressed.<br />
<br />
===Andrei Tarfulea===<br />
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and<br />
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.<br />
<br />
===Siao-hao Guo===<br />
Analysis of Velázquez's solution to the mean curvature flow with a type II singularity<br />
<br />
Velázquez discovered a solution to the mean curvature flow which develops a type II singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution, the rescaled flow converges in the C^0 sense to a minimal hypersurface which is tangent to Simons' cone at infinity. In this talk, we will present that the rescaled flow actually converges locally smoothly to the minimal hypersurface, which appears to be the singularity model of the type II singularity. In addition, we will show that the mean curvature of the solution blows up near the origin at a rate which is smaller than that of the second fundamental form. This is a joint work with N. Sesum.</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13519Colloquia2017-03-16T21:18:32Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29: Sylvia Serfaty (NYU) ===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13518Colloquia2017-03-16T21:16:07Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# Wednesday, March 29 at 3:30PM (Wasow)| Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
=== Friday, March 17: Lillian Pierce (Duke University) ===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29 at 3:30PM (Wasow): Sylvia Serfaty (NYU)===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13509Colloquia2017-03-13T16:18:27Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17, B239<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| p-torsion in class groups of number fields of arbitrary degree<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# Wednesday, March 29 at 3:30PM (Wasow)| Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
===Friday, March 17 at 4:00pm: Lillian Pierce (Duke)===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29 at 3:30PM (Wasow): Sylvia Serfaty (NYU)===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13508Colloquia2017-03-13T15:59:05Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM, 9th floor'''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| p-torsion in class groups of number fields of arbitrary degree<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# Wednesday, March 29 at 3:30PM (Wasow)| Microscopic description of Coulomb-type systems ]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
===Friday, March 17 at 4:00pm: Lillian Pierce (Duke)===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29 at 3:30PM (Wasow): Sylvia Serfaty (NYU)===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13441Colloquia2017-03-01T16:48:34Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13386Colloquia2017-02-17T02:41:11Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13385Colloquia2017-02-16T21:59:01Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, B239<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13384Colloquia2017-02-16T21:27:27Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, B239<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[# TBA| TBA]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13383Colloquia2017-02-16T21:25:54Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[# TBA| TBA]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13362Colloquia2017-02-14T20:00:08Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=13358Colloquia2017-02-14T19:39:36Z<p>Feldman: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a univer