https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Jeffv&feedformat=atomUW-Math Wiki - User contributions [en]2020-02-25T00:41:20ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13289PDE Geometric Analysis seminar2017-02-06T20:23:03Z<p>Jeffv: /* PDE GA Seminar Schedule Spring 2017 */</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<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Wasow lecture<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 />
| <br />
|<br />
| <br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Applied math/PDE/Analysis seminar<br />
| Roger Temam (Indiana University) <br />
|[[#| ]]<br />
| Mathematics Department Distinguished Lecture <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Applied math/PDE/Analysis seminar<br />
| Roger Temam (Indiana University) <br />
|[[#| ]]<br />
| Mathematics Department Distinguished Lecture <br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | ]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Tran<br />
<br />
|-<br />
|March 29<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Wasow lecture<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 />
|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 />
<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 />
===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 />
===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.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13288PDE Geometric Analysis seminar2017-02-06T20:22:45Z<p>Jeffv: /* PDE GA Seminar Schedule Spring 2017 */</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<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Wasow lecture<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 />
| <br />
|[[ ]]<br />
| <br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Applied math/PDE/Analysis seminar<br />
| Roger Temam (Indiana University) <br />
|[[#| ]]<br />
| Mathematics Department Distinguished Lecture <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Applied math/PDE/Analysis seminar<br />
| Roger Temam (Indiana University) <br />
|[[#| ]]<br />
| Mathematics Department Distinguished Lecture <br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | ]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Tran<br />
<br />
|-<br />
|March 29<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Wasow lecture<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 />
|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 />
<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 />
===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 />
===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.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=13034Colloquia/Fall182017-01-18T15:06:13Z<p>Jeffv: </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 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|Directed paths: from Ramsey to Pseudorandomness<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|[[#Monday, December 5: Botong Wang (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]<br />
|Maxim<br />
|<br />
|-<br />
|December 9, B239<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<br />
|-<br />
|'''Monday, December 19, B115'''<br />
| [http://math.uchicago.edu/~andrew.zimmer/ Andrew Zimmer] (U Chicago)<br />
| Metric spaces of non-positive curvature and applications in several complex variables <br />
|Gong<br />
|}<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<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<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<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 (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<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 />
|[[# TBA| TBA ]]<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 (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 />
== 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 />
<br />
== Past Colloquia ==<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>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=13033Analysis Seminar2017-01-18T12:47:35Z<p>Jeffv: </p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
[http://www.math.wisc.edu/~seeger/curr.html Current Semester]<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Andreas at seeger(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule Spring 2017 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 17, Math Department Colloquium<br />
| Fabio Pusateri (Princeton) <br />
|[[#linktoabstract | The Water Waves Problem ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 24, Joint Analysis/Geometry Seminar<br />
| Tamás Darvas (Maryland) <br />
|[[#Tamás Darvas (Maryland) | Existence of constant scalar curvature Kahler metrics and properness of the K-energy ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|Monday, January 30, 3:30, VV901 (PDE Seminar)<br />
| Serguei Denissov (UW)<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 7, Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|Wednesday, March 8, Joint Applied Math/PDE/Analysis Seminar<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|March 14<br />
| Xianghong Chen (UW Milwaukee)<br />
|[[#linktoabstract | Restricting the Fourier transform to some oscillating curves ]]<br />
| Seeger<br />
|<br />
|-<br />
|March 21<br />
| SPRING BREAK<br />
|[[#linktoabstract | ]]<br />
|-<br />
|March 28<br />
| Brian Cook (Fields Institute)<br />
|[[#linktoabstract |TBA ]]<br />
| Seeger<br />
|}<br />
<br />
=Abstracts=<br />
<br />
=== 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 />
=== Tamás Darvas (Maryland) ===<br />
''Existence of constant scalar curvature Kahler metrics and properness of the K-energy''<br />
<br />
Given a compact Kahler manifold $(X,\omega)$, we show that if there exists a constant<br />
scalar curvature Kahler metric cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an<br />
appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful<br />
study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is<br />
joint work with Robert Berman and Chinh H. Lu.<br />
<br />
=== Xianghong Chen (UW Milwaukee) ===<br />
''Restricting the Fourier transform to some oscillating curves''<br />
<br />
I will talk about Fourier restriction to some compact smooth curves. The problem is relatively well understood for curves with nonvanishing torsion due to work of Drury from the 80's, but is less so for curves that contain 'flat' points (i.e. vanishing torsion). Sharp results are known for some monomial-like or finite type curves by work of Bak-Oberlin-Seeger, Dendrinos-Mueller, and Stovall, where a geometric inequality (among others) plays an important role. Such an inequality fails to hold if the torsion demonstrates strong sign-changing behavior, in which case endpoint restriction bounds may fail. In this talk I will present how one could obtain sharp non-endpoint results for certain space curves of this kind. Our approach uses a covering lemma for smooth functions that strengthens a variation bound of Sjolin, who used it to obtain a similar result for plane curves. This is joint work with Dashan Fan and Lifeng Wang.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=13032Analysis Seminar2017-01-18T12:45:45Z<p>Jeffv: </p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
[http://www.math.wisc.edu/~seeger/curr.html Current Semester]<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Andreas at seeger(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule Spring 2017 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 17, Math Department Colloquium<br />
| Fabio Pusateri (Princeton) <br />
|[[#linktoabstract | The Water Waves Problem ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 24<br />
| Tamás Darvas (Maryland) <br />
|[[#Tamás Darvas (Maryland) | Existence of constant scalar curvature Kahler metrics and properness of the K-energy ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|Monday, January 30, 3:30, VV901 (PDE Seminar)<br />
| Serguei Denissov (UW)<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 7, Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|Wednesday, March 8, Joint Applied Math/PDE/Analysis Seminar<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|March 14<br />
| Xianghong Chen (UW Milwaukee)<br />
|[[#linktoabstract | Restricting the Fourier transform to some oscillating curves ]]<br />
| Seeger<br />
|<br />
|-<br />
|March 21<br />
| SPRING BREAK<br />
|[[#linktoabstract | ]]<br />
|-<br />
|March 28<br />
| Brian Cook (Fields Institute)<br />
|[[#linktoabstract |TBA ]]<br />
| Seeger<br />
|}<br />
<br />
=Abstracts=<br />
<br />
=== 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 />
=== Tamás Darvas (Maryland) ===<br />
''Existence of constant scalar curvature Kahler metrics and properness of the K-energy''<br />
<br />
Given a compact Kahler manifold $(X,\omega)$, we show that if there exists a constant<br />
scalar curvature Kahler metric cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an<br />
appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful<br />
study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is<br />
joint work with Robert Berman and Chinh H. Lu.<br />
<br />
=== Xianghong Chen (UW Milwaukee) ===<br />
''Restricting the Fourier transform to some oscillating curves''<br />
<br />
I will talk about Fourier restriction to some compact smooth curves. The problem is relatively well understood for curves with nonvanishing torsion due to work of Drury from the 80's, but is less so for curves that contain 'flat' points (i.e. vanishing torsion). Sharp results are known for some monomial-like or finite type curves by work of Bak-Oberlin-Seeger, Dendrinos-Mueller, and Stovall, where a geometric inequality (among others) plays an important role. Such an inequality fails to hold if the torsion demonstrates strong sign-changing behavior, in which case endpoint restriction bounds may fail. In this talk I will present how one could obtain sharp non-endpoint results for certain space curves of this kind. Our approach uses a covering lemma for smooth functions that strengthens a variation bound of Sjolin, who used it to obtain a similar result for plane curves. This is joint work with Dashan Fan and Lifeng Wang.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=13031Analysis Seminar2017-01-18T12:44:50Z<p>Jeffv: /* Analysis Seminar Schedule Spring 2017 */</p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
[http://www.math.wisc.edu/~seeger/curr.html Current Semester]<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Andreas at seeger(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule Spring 2017 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 17, Math Department Colloquium<br />
| Fabio Pusateri (Princeton) <br />
|[[#linktoabstract | The Water Waves Problem ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 24<br />
| Tamás Darvas (Maryland) <br />
|[[#Darvas | Existence of constant scalar curvature Kahler metrics and properness of the K-energy ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|Monday, January 30, 3:30, VV901 (PDE Seminar)<br />
| Serguei Denissov (UW)<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 7, Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|Wednesday, March 8, Joint Applied Math/PDE/Analysis Seminar<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|March 14<br />
| Xianghong Chen (UW Milwaukee)<br />
|[[#linktoabstract | Restricting the Fourier transform to some oscillating curves ]]<br />
| Seeger<br />
|<br />
|-<br />
|March 21<br />
| SPRING BREAK<br />
|[[#linktoabstract | ]]<br />
|-<br />
|March 28<br />
| Brian Cook (Fields Institute)<br />
|[[#linktoabstract |TBA ]]<br />
| Seeger<br />
|}<br />
<br />
=Abstracts=<br />
<br />
=== 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 />
=== Tamás Darvas (Maryland) ===<br />
''Existence of constant scalar curvature Kahler metrics and properness of the K-energy''<br />
<br />
Given a compact Kahler manifold $(X,\omega)$, we show that if there exists a constant<br />
scalar curvature Kahler metric cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an<br />
appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful<br />
study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is<br />
joint work with Robert Berman and Chinh H. Lu.<br />
<br />
=== Xianghong Chen (UW Milwaukee) ===<br />
''Restricting the Fourier transform to some oscillating curves''<br />
<br />
I will talk about Fourier restriction to some compact smooth curves. The problem is relatively well understood for curves with nonvanishing torsion due to work of Drury from the 80's, but is less so for curves that contain 'flat' points (i.e. vanishing torsion). Sharp results are known for some monomial-like or finite type curves by work of Bak-Oberlin-Seeger, Dendrinos-Mueller, and Stovall, where a geometric inequality (among others) plays an important role. Such an inequality fails to hold if the torsion demonstrates strong sign-changing behavior, in which case endpoint restriction bounds may fail. In this talk I will present how one could obtain sharp non-endpoint results for certain space curves of this kind. Our approach uses a covering lemma for smooth functions that strengthens a variation bound of Sjolin, who used it to obtain a similar result for plane curves. This is joint work with Dashan Fan and Lifeng Wang.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=13030Analysis Seminar2017-01-18T12:43:38Z<p>Jeffv: </p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
[http://www.math.wisc.edu/~seeger/curr.html Current Semester]<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Andreas at seeger(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule Spring 2017 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 17, Math Department Colloquium<br />
| Fabio Pusateri (Princeton) <br />
|[[#linktoabstract | The Water Waves Problem ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 24<br />
| Tamás Darvas (Maryland) <br />
|[[#linktoabstract | Existence of constant scalar curvature Kahler metrics and properness of the K-energy ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|Monday, January 30, 3:30, VV901 (PDE Seminar)<br />
| Serguei Denissov (UW)<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 7, Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|Wednesday, March 8, Joint Applied Math/PDE/Analysis Seminar<br />
| Roger Temam (Indiana) <br />
|[[#linktoabstract | TBA ]]<br />
| Smith<br />
|-<br />
|March 14<br />
| Xianghong Chen (UW Milwaukee)<br />
|[[#linktoabstract | Restricting the Fourier transform to some oscillating curves ]]<br />
| Seeger<br />
|<br />
|-<br />
|March 21<br />
| SPRING BREAK<br />
|[[#linktoabstract | ]]<br />
|-<br />
|March 28<br />
| Brian Cook (Fields Institute)<br />
|[[#linktoabstract |TBA ]]<br />
| Seeger<br />
|}<br />
<br />
=Abstracts=<br />
<br />
=== 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 />
=== Tamás Darvas (Maryland) ===<br />
''Existence of constant scalar curvature Kahler metrics and properness of the K-energy''<br />
<br />
Given a compact Kahler manifold $(X,\omega)$, we show that if there exists a constant<br />
scalar curvature Kahler metric cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an<br />
appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful<br />
study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is<br />
joint work with Robert Berman and Chinh H. Lu.<br />
<br />
=== Xianghong Chen (UW Milwaukee) ===<br />
''Restricting the Fourier transform to some oscillating curves''<br />
<br />
I will talk about Fourier restriction to some compact smooth curves. The problem is relatively well understood for curves with nonvanishing torsion due to work of Drury from the 80's, but is less so for curves that contain 'flat' points (i.e. vanishing torsion). Sharp results are known for some monomial-like or finite type curves by work of Bak-Oberlin-Seeger, Dendrinos-Mueller, and Stovall, where a geometric inequality (among others) plays an important role. Such an inequality fails to hold if the torsion demonstrates strong sign-changing behavior, in which case endpoint restriction bounds may fail. In this talk I will present how one could obtain sharp non-endpoint results for certain space curves of this kind. Our approach uses a covering lemma for smooth functions that strengthens a variation bound of Sjolin, who used it to obtain a similar result for plane curves. This is joint work with Dashan Fan and Lifeng Wang.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=13029Colloquia/Fall182017-01-18T12:38:41Z<p>Jeffv: </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 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|Directed paths: from Ramsey to Pseudorandomness<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|[[#Monday, December 5: Botong Wang (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]<br />
|Maxim<br />
|<br />
|-<br />
|December 9, B239<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<br />
|-<br />
|'''Monday, December 19, B115'''<br />
| [http://math.uchicago.edu/~andrew.zimmer/ Andrew Zimmer] (U Chicago)<br />
| Metric spaces of non-positive curvature and applications in several complex variables <br />
|Gong<br />
|}<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<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'''<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<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<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 (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<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 />
|[[# TBA| TBA ]]<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 (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 />
== 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 />
<br />
== Past Colloquia ==<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>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=13028Colloquia/Fall182017-01-18T12:35:59Z<p>Jeffv: </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 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|Directed paths: from Ramsey to Pseudorandomness<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|[[#Monday, December 5: Botong Wang (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]<br />
|Maxim<br />
|<br />
|-<br />
|December 9, B239<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<br />
|-<br />
|'''Monday, December 19, B115'''<br />
| [http://math.uchicago.edu/~andrew.zimmer/ Andrew Zimmer] (U Chicago)<br />
| Metric spaces of non-positive curvature and applications in several complex variables <br />
|Gong<br />
|}<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<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'''<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<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<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 (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<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 />
|[[# TBA| TBA ]]<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 (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 />
== 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 />
<br />
<br />
== Past Colloquia ==<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>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Fall_2016&diff=12928Fall 20162017-01-01T17:52:43Z<p>Jeffv: </p>
<hr />
<div>= PDE GA Seminar Schedule Spring 2017 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|#date<br />
| #speaker<br />
|[[# | #title ]]<br />
| #host<br />
|-}<br />
<br />
|-<br />
|January 23<br />
| Sigurd Angenent (UW)<br />
|[[# Sigurd Angenent | ]]<br />
| Local<br />
|-}<br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[# Serguei Denissov | ]]<br />
| Local<br />
|-}<br />
<br />
<br />
|-<br />
|February 6<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Wasow lecture<br />
|-}<br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[# Bing Wang | ]]<br />
| Local<br />
|-}<br />
<br />
|-<br />
|February 20<br />
| Hans-Joachim Hein (Fordham)<br />
|[[# Hans-Joachim Hein | ]]<br />
| Viaclovsky<br />
|-}<br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | ]]<br />
| Tran<br />
|-}<br />
<br />
|-<br />
|March 7 - Applied math/PDE/Analysis seminar<br />
| Roger Temam (Indiana University) <br />
|[[#| ]]<br />
| Mathematics Department Distinguished Lecture <br />
|-}<br />
<br />
<br />
|-<br />
|March 8 - Applied math/PDE/Analysis seminar<br />
| Roger Temam (Indiana University) <br />
|[[#| ]]<br />
| Mathematics Department Distinguished Lecture <br />
|-}<br />
<br />
<br />
|-<br />
|March 27<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Tran<br />
<br />
|-<br />
|March 29<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Wasow lecture<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Fall_2016&diff=12789Fall 20162016-12-01T02:58:58Z<p>Jeffv: </p>
<hr />
<div>= PDE GA Seminar Schedule Spring 2017 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|#date<br />
| #speaker<br />
|[[# | #title ]]<br />
| #host<br />
|-}<br />
<br />
|-<br />
|January 23<br />
| Sigurd Angenent (UW)<br />
|[[# Sigurd Angenent | ]]<br />
| Local<br />
|-}<br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[# Serguei Denissov | ]]<br />
| Local<br />
|-}<br />
<br />
|-<br />
|February 6<br />
| Myoungjean Bae (POSTECH)<br />
|[[# Myoungjean Bae | ]]<br />
| Feldman<br />
|-}<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[# Bing Wang | ]]<br />
| Local<br />
|-}<br />
<br />
|-<br />
|February 20<br />
| Hans-Joachim Hein (Fordham)<br />
|[[# Hans-Joachim Hein | ]]<br />
| Viaclovsky<br />
|-}<br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | ]]<br />
| Tran<br />
|-}<br />
<br />
|-<br />
|March 6<br />
| No seminar because of Distinguished lectures by Temam on March 7 and March 8.<br />
|[[#| ]]<br />
| <br />
|-}<br />
<br />
<br />
|-<br />
|March 27<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Tran</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12779Geometry and Topology Seminar2016-11-29T20:39:14Z<p>Jeffv: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|<br />
| <br />
|-<br />
|<br />
|}<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 />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "TBA"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12174Geometry and Topology Seminar2016-09-02T19:10:21Z<p>Jeffv: /* Fall 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| Gauduchon metrics with prescribed volume form]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "TBA"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "TBA"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "TBA"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| <br />
| <br />
| <br />
|-<br />
|October 28<br />
| Ronan Conlon<br />
| [[#Ronan Conlon| "TBA"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|'''November 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| <br />
| <br />
| <br />
|-<br />
|November 18<br />
| <br />
| <br />
| <br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''TBA''<br />
<br />
=== Jiyuan Han ===<br />
''TBA''<br />
<br />
=== Sean Howe ===<br />
''TBA''<br />
<br />
===Yu Li ===<br />
''TBA''<br />
<br />
===Gaven Marin ===<br />
''TBA''<br />
<br />
===Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''TBA''<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12173Geometry and Topology Seminar2016-09-02T19:07:15Z<p>Jeffv: /* Fall Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| Gauduchon metrics with prescribed volume form]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "TBA"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "TBA"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "TBA"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| <br />
| <br />
| <br />
|-<br />
|October 28<br />
| Ronan Conlon<br />
| [[#Ronan Conlon| "TBA"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|'''November 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| <br />
| <br />
| <br />
|-<br />
|November 18<br />
| <br />
| <br />
| <br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| Jeff Viaclovsky <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''TBA''<br />
<br />
=== Jiyuan Han ===<br />
''TBA''<br />
<br />
=== Sean Howe ===<br />
''TBA''<br />
<br />
===Yu Li ===<br />
''TBA''<br />
<br />
===Gaven Marin ===<br />
''TBA''<br />
<br />
===Peyman Morteza ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''TBA''<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12172Geometry and Topology Seminar2016-09-02T19:06:32Z<p>Jeffv: /* Fall 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| Gauduchon metrics with prescribed volume form]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "TBA"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "TBA"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "TBA"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| <br />
| <br />
| <br />
|-<br />
|October 28<br />
| Ronan Conlon<br />
| [[#Ronan Conlon| "TBA"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|'''November 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| <br />
| <br />
| <br />
|-<br />
|November 18<br />
| <br />
| <br />
| <br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| Jeff Viaclovsky <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''TBA''<br />
<br />
=== Jiyuan Han ===<br />
''TBA''<br />
<br />
=== Sean Howe ===<br />
''TBA''<br />
<br />
===Yu Li ===<br />
''TBA''<br />
<br />
===Gaven Marin ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''TBA''<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12171Geometry and Topology Seminar2016-09-02T19:06:06Z<p>Jeffv: /* Fall 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| Gauduchon metrics with prescribed volume form]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "TBA"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "TBA"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "TBA"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| <br />
| <br />
| <br />
|-<br />
|October 28<br />
| Ronan Conlon<br />
| [[#Ronan Conlon| "TBA"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|'''November 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| <br />
| <br />
| <br />
|-<br />
|November 18<br />
| <br />
| <br />
| <br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW)<br />
| [[#Peyman Morteza| "TBA"]]<br />
| Jeff Viaclovsky <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''TBA''<br />
<br />
=== Jiyuan Han ===<br />
''TBA''<br />
<br />
=== Sean Howe ===<br />
''TBA''<br />
<br />
===Yu Li ===<br />
''TBA''<br />
<br />
===Gaven Marin ===<br />
''TBA''<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''TBA''<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=7999PDE Geometric Analysis seminar2014-08-20T02:09:18Z<p>Jeffv: /* Seminar Schedule Fall 2014 */</p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
<br />
= Seminar Schedule Fall 2013 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Greg Drugan (U. of Washington)<br />
|[[#Greg Drugan (U. of Washington) |<br />
Construction of immersed self-shrinkers]]<br />
|Angenent<br />
|-<br />
|-<br />
|October 7<br />
|[http://users.cms.caltech.edu/~gluo/ Guo Luo (Caltech)]<br />
|[[#Guo Luo (Caltech) |<br />
Potentially Singular Solutions of the 3D Incompressible Euler Equations. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 18<br />
|[http://people.cas.uab.edu/~shterenb/ Roman Shterenberg (UAB)]<br />
|[[#Roman Shterenberg (UAB) |<br />
Recent progress in multidimensional periodic and almost-periodic spectral<br />
problems. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 25<br />
|Myeongju Chae (Hankyong National University visiting UW)<br />
|[[#Myeongju Chae (Hankyong National University) |<br />
On the global classical solution of the Keller-Segel-Navier -Stokes system and its asymptotic behavior. ]]<br />
|Kiselev<br />
|-<br />
myeongju Chae <br />
|-<br />
|December 2<br />
|Xiaojie Wang<br />
|[[#Xiaojie Wang (Stony Brook University) |<br />
Uniqueness of Ricci flow solutions on noncompact manifolds. ]]<br />
|Wang<br />
|-<br />
|-<br />
|December 16<br />
|Antonio Ache(Princeton)<br />
|[[#Antonio Ache(Princeton) |<br />
Ricci Curvature and the manifold learning problem. NOTE: Due to final exams, this seminar will be held in B231. ]]<br />
|Viaclovsky<br />
|-<br />
|}<br />
<br />
= Seminar Schedule Spring 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 14 at 4pm in B139 (TUESDAY), joint with Analysis<br />
|[http://www.math.univ-toulouse.fr/~roque/ Jean-Michel Roquejoffre (Toulouse)]<br />
|[[#Jean-Michel Roquejoffre (Toulouse) |<br />
Front propagation in the presence of integral diffusion. ]]<br />
|Zlatos<br />
|-<br />
|-<br />
|February 10<br />
|[http://math.postech.ac.kr/~mjbae/ Myoungjean Bae (POSTECH)]<br />
|[[#Myoungjean Bae (POSTECH) |<br />
Free Boundary Problem related to Euler-Poisson system. ]]<br />
|Feldman<br />
|-<br />
|-<br />
|February 24<br />
|[http://www2.math.umd.edu/~jefftan/ Changhui Tan (Maryland)]<br />
|[[#Changhui Tan (Maryland) |<br />
Global classical solution and long time behavior of macroscopic flocking models. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|March 3<br />
|[http://www.dam.brown.edu/people/hdong Hongjie Dong (Brown)]<br />
|[[#Hongjie Dong (Brown) |<br />
Parabolic equations in time-varying domains. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|March 10<br />
|[http://math.uchicago.edu/~jiahao/ Hao Jia (University of Chicago)]<br />
|[[#Hao Jia (University of Chicago) |<br />
Long time dynamics of energy critical defocusing wave equation with<br />
radial potential in 3+1 dimensions. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|March 31<br />
|[http://www.mth.kcl.ac.uk/staff/a_pushnitski.html Alexander Pushnitski (King's College London)]<br />
|[[#Alexander Pushnitski (King's College) |<br />
An inverse spectral problem for Hankel operators. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 21<br />
|[http://people.math.gatech.edu/~panrh/ Ronghua Pan (Georgia Tech)]<br />
|[[#Ronghua Pan (Georgia Tech) |<br />
Compressible Navier-Stokes-Fourier system with temperature dependent dissipation. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
= Seminar Schedule Fall 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 15 <br />
|Greg Kuperberg (UC-Davis)<br />
|[[#Greg Kuperberg (UC-Davis) |<br />
TBA]]<br />
|Viaclovsky<br />
|-<br />
|-<br />
|September 22 (joint with Analysis Seminar)<br />
|Steven Hofmann (U. of Missouri)<br />
|[[#Steven Hofmann (U. of Missouri) |<br />
TBA]]<br />
|Seeger<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
<br />
===Greg Drugan (U. of Washington)===<br />
''Construction of immersed self-shrinkers''<br />
<br />
Abstract: We describe a procedure for constructing immersed<br />
self-shrinking solutions to mean curvature flow. <br />
The self-shrinkers we construct have a rotational symmetry, and<br />
the construction involves a detailed study of geodesics in the<br />
upper-half plane with a conformal metric.<br />
This is a joint work with Stephen Kleene.<br />
<br />
===Guo Luo (Caltech)===<br />
''Potentially Singular Solutions of the 3D Incompressible Euler Equations''<br />
<br />
Abstract:<br />
Whether the 3D incompressible Euler equations can develop a singularity in <br />
finite time from smooth initial data is one of the most challenging problems in <br />
mathematical fluid dynamics. This work attempts to provide an affirmative answer to this <br />
long-standing open question from a numerical point of view, by presenting a class of <br />
potentially singular solutions to the Euler equations computed in axisymmetric <br />
geometries. The solutions satisfy a periodic boundary condition along the axial direction <br />
and no-flow boundary condition on the solid wall. The equations are discretized in space <br />
using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially <br />
designed adaptive (moving) meshes that are dynamically adjusted to the evolving <br />
solutions. With a maximum effective resolution of over $(3 \times 10^{12})^{2}$ near the <br />
point of singularity, we are able to advance the solution up to $\tau_{2} = 0.003505$ and <br />
predict a singularity time of $t_{s} \approx 0.0035056$, while achieving a <br />
\emph{pointwise} relative error of $O(10^{-4})$ in the vorticity vector $\omega$ and <br />
observing a $(3 \times 10^{8})$-fold increase in the maximum vorticity <br />
$\norm{\omega}_{\infty}$. The numerical data is checked against all major blowup <br />
(non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and <br />
Deng-Hou-Yu, to confirm the validity of the singularity. A careful local analysis also <br />
suggests that the blowing-up solution develops a self-similar structure near the point of <br />
the singularity, as the singularity time is approached.<br />
<br />
===Xiaojie Wang(Stony Brook)===<br />
''Uniqueness of Ricci flow solutions on noncompact manifolds''<br />
<br />
Abstract:<br />
Ricci flow is an important evolution equation of Riemannian metrics.<br />
Since it was introduced by R. Hamilton in 1982, it has greatly changed the landscape of riemannian geometry. One of the fundamental question about ricci flow is when is its solution to initial value problem unique. On compact manifold, with arbitrary initial metric, it was confirmed by Hamilton. On noncompact manifold, we only know this is true when further restrictions are imposed to the solution. In this talk, we will discuss various conditions that guarantee the uniqueness. In particular, we will discuss in details with the following uniqueness result. Let $(M,g)$ be a complete noncompact non-collapsing $n$-dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded from above. Then ricci flow with above as its initial data, on $M\times [0,\epsilon]$ for some $\epsilon>0$, has at most one solution in the class of complete riemannian metric with complex sectional curvature bounded from below.<br />
<br />
===Roman Shterenberg(UAB)===<br />
''Recent progress in multidimensional periodic and almost-periodic spectral<br />
problems''<br />
<br />
Abstract: We present a review of the results in multidimensional periodic<br />
and almost-periodic spectral problems. We discuss some recent progress and<br />
old/new ideas used in the constructions. The talk is mostly based on the<br />
joint works with Yu. Karpeshina and L. Parnovski.<br />
<br />
===Antonio Ache(Princeton)===<br />
''Ricci Curvature and the manifold learning problem''<br />
<br />
Abstract: In the first half of this talk we will review several notions of coarse or weak<br />
Ricci Curvature on metric measure spaces which include the works of Lott-Villani, Sturm<br />
and Ollivier. The discussion of the notion of coarse Ricci curvature will serve as <br />
motivation for developing a method to estimate the Ricci curvature of a an embedded<br />
submaifold of Euclidean space from a point cloud which has applications to the Manifold<br />
Learning Problem. Our method is based on combining the notion of ``Carre du Champ"<br />
introduced by Bakry-Emery with a result of Belkin and Niyogi which shows that it is<br />
possible to recover the rough laplacian of embedded submanifolds of the Euclidean space<br />
from point clouds. This is joint work with Micah Warren.<br />
<br />
===Jean-Michel Roquejoffre (Toulouse)===<br />
''Front propagation in the presence of integral diffusion''<br />
<br />
Abstract: In many reaction-diffusion equations, where diffusion is<br />
given by a second order elliptic operator, the solutions<br />
will exhibit spatial transitions whose velocity is asymptotically<br />
linear in time. The situation can be different when the diffusion is of the<br />
integral type, the most basic example being the fractional Laplacian:<br />
the velocity can be time-exponential. We will explain why, and<br />
discuss several situations where this type of fast propagation<br />
occurs.<br />
<br />
===Myoungjean Bae (POSTECH)===<br />
''Free Boundary Problem related to Euler-Poisson system''<br />
<br />
One dimensional analysis of Euler-Poisson system shows that when incoming <br />
supersonic flow is fixed, transonic shock can be represented as a monotone <br />
function of exit pressure. From this observation, we expect well-posedness <br />
of transonic shock problem for Euler-Poisson system when exit pressure is <br />
prescribed in a proper range. In this talk, I will present recent progress <br />
on transonic shock problem for Euler-Poisson system, which is formulated <br />
as a free boundary problem with mixed type PDE system. <br />
This talk is based on collaboration with Ben Duan(POSTECH), Chujing Xie(SJTU) <br />
and Jingjing Xiao(CUHK).<br />
<br />
===Changhui Tan (University of Maryland)===<br />
''Global classical solution and long time behavior of macroscopic flocking models''<br />
<br />
Abstract: Self-organized behaviors are very common in nature and human societies.<br />
One widely discussed example is the flocking phenomenon which describes<br />
animal groups emerging towards the same direction. Several models such<br />
as Cucker-Smale and Motsch-Tadmor are very successful in characterizing<br />
flocking behaviors. In this talk, we will discuss macroscopic representation<br />
of flocking models. These systems can be interpreted as compressible Eulerian <br />
dynamics with nonlocal alignment forcing. We show global existence of classical solutions and long time <br />
flocking behavior of the system, when initial profile satisfies a threshold condition. On the other hand, another set<br />
of initial conditions will lead to a finite time break down of the system. This<br />
is a joint work with Eitan Tadmor.<br />
<br />
===Hongjie Dong (Brown University)===<br />
''Parabolic equations in time-varying domains''<br />
<br />
Abstract: I will present a recent result on the Dirichlet boundary value<br />
problem for parabolic equations in time-varying domains. The equations are<br />
in either divergence or non-divergence form with boundary blowup low-order<br />
coefficients. The domains satisfy an exterior measure condition.<br />
<br />
===Hao Jia (University of Chicago)===<br />
''Long time dynamics of energy critical defocusing wave equation with<br />
radial potential in 3+1 dimensions.''<br />
<br />
Abstract: We consider the long term dynamics of radial solution to the<br />
above mentioned equation. For general potential, the equation can have a<br />
unique positive ground state and a number of excited states. One can expect<br />
that some solutions might stay for very long time near excited states<br />
before settling down to an excited state of lower energy or the ground<br />
state. Thus the detailed dynamics can be extremely complicated. However<br />
using the ``channel of energy" inequality discovered by T.Duyckaerts,<br />
C.Kenig and F.Merle, we can show for generic potential, any radial solution<br />
is asymptotically the sum of a free radiation and a steady state as time<br />
goes to infinity. This provides another example of the power of ``channel<br />
of energy" inequality and the method of profile decompositions. I will<br />
explain the basic tools in some detail. Joint work with Baoping Liu and<br />
Guixiang Xu.<br />
<br />
===Alexander Pushnitski (King's College)===<br />
''An inverse spectral problem for Hankel operators''<br />
<br />
Abstract:<br />
I will discuss an inverse spectral problem for a certain class of Hankel<br />
operators. The problem appeared in the recent work by P.Gerard and S.Grellier as a<br />
step towards description of evolution in a model integrable non-dispersive<br />
equation. Several features of this inverse problem make it strikingly (and somewhat<br />
mysteriously) similar to an inverse problem for Sturm-Liouville operators. I will<br />
describe the available results for Hankel operators, emphasizing this similarity.<br />
This is joint work with Patrick Gerard (Orsay).<br />
<br />
===Ronghua Pan (Georgia Tech)===<br />
''Compressible Navier-Stokes-Fourier system with temperature dependent dissipation''<br />
<br />
Abstract: From its physical origin such as Chapman-Enskog or Sutherland, the viscosity and<br />
heat conductivity coefficients in compressible fluids depend on absolute temperature<br />
through power laws. The mathematical theory on the well-posedness and regularity on this<br />
setting is widely open. I will report some recent progress on this direction,<br />
with emphasis on the lower bound of temperature, and global existence of<br />
solutions in one or multiple dimensions. The relation between thermodynamics laws<br />
and Navier-Stokes-Fourier system will also be discussed. This talk is based on joint works<br />
with Junxiong Jia and Weizhe Zhang.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3193Geometry and Topology Seminar2011-12-01T16:25:18Z<p>Jeffv: /* Bing Wang (Simons Center for Geometry and Physics) */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1 at 2 PM in Ingraham 114<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties.''<br />
NOTE SPECIAL PLACE AND TIME: Thursday, December 1 at 2 PM in Ingraham 114.]]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This will be a more detailed version of<br />
the speaker's colloquium talk.<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''Ricci Flow, Analytic Stability, and the Space of Kähler Metrics''<br />
<br />
I will consider the space of all Kähler metrics on a fixed, compact, complex manifold as a submanifold of the manifold of all Riemannian metrics. The geometry induced on it in this way coincides with a Riemannian metric first defined by Calabi in the 1950s. After giving a detailed study of the Riemannian distance function - in particular determining the completion of the space of Kähler metrics - I will give a new analytic stability criterion for the existence of a Kähler--Einstein metric on a Fano manifold in terms of the Ricci flow and the distance function. Additionally, I will describe a result showing that the Kähler--Ricci flow converges as soon as it converges in the very weak metric sense. This is joint work with Yanir Rubinstein.<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3192Geometry and Topology Seminar2011-12-01T16:24:52Z<p>Jeffv: /* Bing Wang (Simons Center for Geometry and Physics) */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1 at 2 PM in Ingraham 114<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties.''<br />
NOTE SPECIAL PLACE AND TIME: Thursday, December 1 at 2 PM in Ingraham 114.]]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This will be a technical version of<br />
the speaker's colloquium talk.<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''Ricci Flow, Analytic Stability, and the Space of Kähler Metrics''<br />
<br />
I will consider the space of all Kähler metrics on a fixed, compact, complex manifold as a submanifold of the manifold of all Riemannian metrics. The geometry induced on it in this way coincides with a Riemannian metric first defined by Calabi in the 1950s. After giving a detailed study of the Riemannian distance function - in particular determining the completion of the space of Kähler metrics - I will give a new analytic stability criterion for the existence of a Kähler--Einstein metric on a Fano manifold in terms of the Ricci flow and the distance function. Additionally, I will describe a result showing that the Kähler--Ricci flow converges as soon as it converges in the very weak metric sense. This is joint work with Yanir Rubinstein.<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3183Geometry and Topology Seminar2011-11-30T21:05:26Z<p>Jeffv: /* Brian Clarke (Stanford) */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1 at 2 PM in Ingraham 114<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties.''<br />
NOTE SPECIAL PLACE AND TIME: Thursday, December 1 at 2 PM in Ingraham 114.]]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This is will be a technical version of<br />
the speaker's colloquium talk.<br />
<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''Ricci Flow, Analytic Stability, and the Space of Kähler Metrics''<br />
<br />
I will consider the space of all Kähler metrics on a fixed, compact, complex manifold as a submanifold of the manifold of all Riemannian metrics. The geometry induced on it in this way coincides with a Riemannian metric first defined by Calabi in the 1950s. After giving a detailed study of the Riemannian distance function - in particular determining the completion of the space of Kähler metrics - I will give a new analytic stability criterion for the existence of a Kähler--Einstein metric on a Fano manifold in terms of the Ricci flow and the distance function. Additionally, I will describe a result showing that the Kähler--Ricci flow converges as soon as it converges in the very weak metric sense. This is joint work with Yanir Rubinstein.<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3160Colloquia 2012-20132011-11-28T21:14:00Z<p>Jeffv: /* Wed, Nov 30: Bing Wang (Simons Center for Geometry and Physics) */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Wed, Nov 30: Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety.<br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3159Colloquia 2012-20132011-11-28T21:13:35Z<p>Jeffv: /* Wed, Nov 30: Bing Wang (Simons Center for Geometry and Physics) */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Wed, Nov 30: Bing Wang (Simons Center for Geometry and Physics)===<br />
"Uniformization of algebraic varieties"<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety.<br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3158Colloquia 2012-20132011-11-28T21:13:07Z<p>Jeffv: /* Wed, November 30: Bing Wang (Simons Center for Geometry and Physics) */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Wed, Nov 30: Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety.<br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3157Colloquia 2012-20132011-11-28T21:12:57Z<p>Jeffv: /* Wednesday, November 30: Bing Wang (Simons Center for Geometry and Physics) */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Wed, November 30: Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety.<br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3156Colloquia 2012-20132011-11-28T21:12:45Z<p>Jeffv: /* Bing Wang (Simons Center for Geometry and Physics) */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Wednesday, November 30: Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety.<br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3155Colloquia 2012-20132011-11-28T21:11:47Z<p>Jeffv: /* Abstracts */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. <br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia_2012-2013&diff=3154Colloquia 2012-20132011-11-28T21:10:28Z<p>Jeffv: /* Fall 2011 */</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 />
== Fall 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 9<br />
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)<br />
|''Periodic orbits on homogeneous spaces''<br />
|Fish<br />
|-<br />
|Sep 16<br />
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)<br />
|''Global singularity theory''<br />
|Maxim<br />
|-<br />
|Sep 23<br />
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)<br />
|''The Pfaffian-Grassmannian derived equivalence''<br />
|(local)<br />
|-<br />
|Sep 30<br />
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)<br />
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
|(local)<br />
|-<br />
|Oct 7<br />
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)<br />
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
|Lempp<br />
|-<br />
|Oct 14<br />
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)<br />
|''On Zaremba's Conjecture''<br />
|Shamgar<br />
|-<br />
|'''oct 19, Wed'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Convex Algebraic Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|'''oct 20, Thu'''<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Quartic Curves and Their Bitangents''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|oct 21<br />
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)<br />
|''Multiview Geometry''<br />
|'''distinguished lecturer'''<br />
|Shamgar <br />
|-<br />
|Oct 28<br />
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)<br />
|''Equidistribution Problems and L-functions''<br />
|Street<br />
|-<br />
|Nov 4<br />
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)<br />
|''Wellposedness of the two and three dimensional full water wave problem''<br />
|Qin Li<br />
|-<br />
|'''Nov 7, Mo, 3pm, SMI 133'''<br />
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)<br />
|''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
|'''Joint Math/Stat Colloquium''' <br />
|-<br />
|Nov 11<br />
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)<br />
|''Reaction-diffusion equations and propagation phenomena''<br />
|'''Wasow lecture'''<br />
|-<br />
|'''Nov 16, Wed'''<br />
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)<br />
|''An Analytic Approach to Uniformity Norms''<br />
|Steffen <br />
|-<br />
|Nov 18<br />
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)<br />
|''The Convex Geometry of Inverse Problems''<br />
|Jordan<br />
|-<br />
|'''Nov 22, Tue, 2:30PM, B205'''<br />
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)<br />
|''Motives and the inverse Galois problem''<br />
|Tonghai <br />
|-<br />
|'''Nov 28, Mon, 4PM'''<br />
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)<br />
|''Analytic knots, satellites and the 4-ball genus''<br />
|Gong<br />
|-<br />
|'''Nov 29, Tue, 2:30PM, B102'''<br />
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)<br />
|"Nonstandard methods in Lie theory"<br />
|Lempp <br />
|-<br />
|'''Nov 30, Wed, 4PM'''<br />
|Bing Wang (Simons Institute)<br />
|''Uniformization of algebraic varieties''<br />
|Sean <br />
|-<br />
|Dec 2<br />
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)<br />
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''<br />
|Jean-Luc<br />
|-<br />
|'''Dec 5, Mon, 2:25PM, Room 901'''<br />
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)<br />
|''TBA''<br />
|Andrei <br />
|-<br />
|'''Dec 7, Wed, 4PM'''<br />
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)<br />
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''<br />
|Misha Feldman <br />
|-<br />
|Dec 9<br />
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)<br />
|''TBA''<br />
|Tonghai<br />
|}<br />
<br />
== Spring 2012 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Jan 26, Thu'''<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Jan 27<br />
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|Feb 3<br />
|''Scheduled''<br />
|<br />
|Street<br />
|-<br />
|Feb 24<br />
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)<br />
|''TBA''<br />
|Benguria<br />
|-<br />
|March 2<br />
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)<br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|March 16<br />
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)<br />
|''TBA''<br />
|Matt Ballard<br />
|-<br />
|March 23<br />
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)<br />
|''TBA''<br />
|Don Passman<br />
|-<br />
|March 30<br />
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|April 6<br />
|Spring recess <br />
|<br />
|<br />
|-<br />
|April 13<br />
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)<br />
|''TBA''<br />
|Mitchell<br />
|-<br />
|April 18<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 19<br />
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)<br />
|''TBA''<br />
|'''distinguished lecturer'''<br />
|-<br />
|April 20<br />
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California) <br />
|''TBA''<br />
|Shamgar<br />
|-<br />
|April 27<br />
|''Tentatively Scheduled''<br />
|<br />
|Street<br />
|-<br />
|May 4<br />
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)<br />
|''TBA''<br />
|Maxim<br />
|-<br />
|May 11<br />
|''Tentatively Scheduled''<br />
|<br />
|Shamgar<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===<br />
''Periodic orbits on homogeneous spaces''<br />
<br />
We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G<br />
periodic if it has finite H-invariant volume. These orbits have<br />
intimate connections to a variety of number theoretic problems, e.g.<br />
both integer quadratic forms and number fields give rise periodic<br />
orbits and these periodic orbits then relate to local-global problems<br />
for the quadratic forms or to special values of L-functions. We will<br />
discuss whether a sequence of periodic orbits equidistribute in Gamma<br />
\ G assuming the orbits become more complicated (which can be measured<br />
by a discriminant). If H is a diagonal subgroup (also called torus or<br />
Cartan subgroup), this is not always the case but can be true with a<br />
bit more averaging. As a theorem of Mozes and Shah show the case where<br />
H is generated by unipotents is well understand and is closely related<br />
to the work of M. Ratner. We then ask about the rate of approximation,<br />
where the situation is much more complex. The talk is based on several<br />
papers which are joint work with E.Lindenstrauss, Ph. Michel, and A.<br />
Venkatesh resp. with G. Margulis and A. Venkatesh.<br />
<br />
===Fri, Sept 16: Richard Rimanyi (UNC)===<br />
''Global singularity theory''<br />
<br />
The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. <br />
<br />
To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.<br />
<br />
===Fri, Sept 23: Andrei Caldararu (UW-Madison)===<br />
''The Pfaffian-Grassmannian derived equivalence''<br />
<br />
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!<br />
<br />
===Fri, Sept 30: Scott Armstrong (UW-Madison)===<br />
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''<br />
<br />
Given a nice bounded domain, and a Lipschitz function<br />
defined on its boundary, consider the problem of finding an extension<br />
of this function to the closure of the domain which has minimal<br />
Lipschitz constant. This is the archetypal problem of the calculus of<br />
variations<br />
"in the sup-norm". There can be many such minimal Lipschitz<br />
extensions, but there is there is a unique minimizer once we properly<br />
"localize" this Lipschitz minimizing property. This minimizer is<br />
characterized by the infinity Laplace equation: the Euler-Lagrange<br />
equation for our optimization problem. This PDE is a very highly<br />
degenerate nonlinear elliptic equation which does not possess smooth<br />
solutions in general. In this talk I will discuss what we know about<br />
the infinity Laplace equation, what the important open questions are,<br />
and some interesting recent developments. We will even play a<br />
probabilistic game called "tug-of-war".<br />
<br />
===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===<br />
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''<br />
<br />
Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.<br />
<br />
===Fri, Oct 14: Alex Kontorovich (Yale)===<br />
''On Zaremba's Conjecture''<br />
<br />
It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.<br />
<br />
===Wed, Oct 19: Bernd Sturmfels (Berkeley)===<br />
''Convex Algebraic Geometry''<br />
<br />
This lecture concerns convex bodies with an interesting algebraic structure.<br />
A primary focus lies on the geometry of semidefinite optimization. Starting<br />
with elementary questions about ellipses in the plane, we move on to discuss<br />
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.<br />
<br />
===Thu, Oct 20: Bernd Sturmfels (Berkeley)===<br />
''Quartic Curves and Their Bitangents''<br />
<br />
We present a computational study of plane curves of degree four, with<br />
primary focus on writing their defining polynomials as sums of squares<br />
and as symmetric determinants. Number theorists will enjoy the appearance<br />
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based<br />
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture<br />
spans a bridge from 19th century algebra to 21st century optimization.<br />
<br />
===Fri, Oct 21: Bernd Sturmfels (Berkeley)===<br />
''Multiview Geometry''<br />
<br />
The study of two-dimensional images of three-dimensional scenes is foundational<br />
for computer vision. We present work with Chris Aholt and Rekha Thomas on the<br />
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are<br />
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are<br />
moving. We use toric geometry and Hilbert schemes to characterize<br />
degenerations of camera positions.<br />
<br />
===Fri, Oct 28: Roman Holowinsky (OSU)===<br />
''Equidistribution Problems and L-functions''<br />
<br />
There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics. We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms. Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.<br />
<br />
===Fri, Nov 4: Sijue Wu (U Michigan)===<br />
''Wellposedness of the two and three dimensional full water wave problem''<br />
<br />
We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.<br />
<br />
===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===<br />
''Opportunities in Mathematical and Statistical Sciences at DMS''<br />
<br />
In this talk, I will give you an overview of the funding and<br />
other opportunities at DMS for mathematicians and statisticians. I will<br />
also talk about our new program in computational and data-enabled science<br />
and engineering in mathematical and statistical sciences (CDS&E-MSS).<br />
<br />
===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===<br />
''Reaction-diffusion equations and propagation phenomena''<br />
<br />
Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.<br />
<br />
===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===<br />
''An Analytic Approach to Uniformity Norms''<br />
<br />
The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects. While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting. We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.<br />
<br />
===Fri, Nov 18: Ben Recht (UW-Madison)===<br />
''The Convex Geometry of Inverse Problems''<br />
<br />
Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.<br />
<br />
In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functions. This approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices. I will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models. I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.<br />
<br />
===Tue, Nov 22: Zhiwei Yun (MIT)===<br />
"Motives and the inverse Galois problem"<br />
<br />
We will use geometric Langlands theory to solve two problems<br />
simultaneously. One is Serre's question about whether there<br />
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other<br />
is whether there are Galois extensions of Q with Galois groups E_8(p)<br />
or G_2(p) (the finite simple groups of Lie type). The answers to both<br />
questions are YES. No familiarity with either motives or geometric<br />
Langlands or E_8 will be assumed.<br />
<br />
===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===<br />
"Analytic knots, satellites and the 4-ball genus"<br />
<br />
After introducing classical geometric knot invariants and satellites<br />
I will concentrate on knots or links in the unit sphere in $\mathbb<br />
C^2$ which bound a complex curve (respectively, a smooth complex<br />
curve) in the unit ball. Such a knot or link will be called analytic<br />
(respectively, smoothly analytic). For analytic satellite links of<br />
smoothly analytic knots there is a sharp lower bound for the 4-ball<br />
genus. It is given in terms of the 4-ball genus of the companion and<br />
the winding number. No such estimate is true in the general case.<br />
There is a natural relation to the theory of holomorphic mappings<br />
from open Riemann surfaces into the space of monic polynomials<br />
without multiple zeros. I will briefly touch related problems.<br />
<br />
===Tue, Nov 29: Isaac Goldbring (UCLA)===<br />
"Nonstandard methods in Lie theory"<br />
<br />
Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular: the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras. I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.<br />
<br />
===Wed, Dec 7: Toan Nguyen (Brown University)===<br />
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"<br />
<br />
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3153Geometry and Topology Seminar2011-11-28T21:07:34Z<p>Jeffv: /* Fall 2011 */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1 at 2 PM in Ingraham 114<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties.''<br />
NOTE SPECIAL PLACE AND TIME: Thursday, December 1 at 2 PM in Ingraham 114.]]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This is will be a technical version of<br />
the speaker's colloquium talk.<br />
<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3152Geometry and Topology Seminar2011-11-28T21:06:59Z<p>Jeffv: /* Fall 2011 */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1 at 2 PM in Ingraham 114<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties''<br />
NOTE SPECIAL PLACE AND TIME: Thursday, December 1 at 2 PM in Ingraham 114]]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This is will be a technical version of<br />
the speaker's colloquium talk.<br />
<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3151Geometry and Topology Seminar2011-11-28T21:05:55Z<p>Jeffv: /* Fall 2011 */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties''<br />
TEST]]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This is will be a technical version of<br />
the speaker's colloquium talk.<br />
<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3150Geometry and Topology Seminar2011-11-28T21:04:38Z<p>Jeffv: /* Abstracts */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties'']]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===Bing Wang (Simons Center for Geometry and Physics)===<br />
''Uniformization of algebraic varieties''<br />
<br />
For algebraic varieties of general type with<br />
mild singularities, we show the Bogmolov-Yau inequality<br />
holds. If equality is attained, then this variety is a<br />
global quotient of complex hyperbolic space away from<br />
a subvariety. This is will be a technical version of<br />
the speaker's colloquium talk.<br />
<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3149Geometry and Topology Seminar2011-11-28T21:03:06Z<p>Jeffv: /* Fall 2011 */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1<br />
| Bing Wang (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)|<br />
''Uniformization of algebraic varieties'']]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3148Geometry and Topology Seminar2011-11-28T21:00:50Z<p>Jeffv: /* Fall 2011 */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1<br />
|[Bing Wang] (Simons Center for Geometry and Physics)<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)<br />
''Uniformization of algebraic varieties'']]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=3147Geometry and Topology Seminar2011-11-28T21:00:01Z<p>Jeffv: /* Fall 2011 */</p>
<hr />
<div>== Fall 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)<br />
|[[#Gloria Mari Beffa (UW Madison)|<br />
''The pentagram map and generalizations: discretizations of AGD flows'']]<br />
|[local]<br />
|-<br />
|September 16<br />
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (University of Minnesota)<br />
|[[#Ke Zhu (University of Minnesota)|<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|September 23<br />
|[http://www.math.wisc.edu/~ache/ Antonio Ache] (UW Madison)<br />
|[[#Antonio Ache (UW Madison)|<br />
''Obstruction-Flat Asymptotically Locally Euclidean Metrics'']]<br />
|[local]<br />
|-<br />
|September 30<br />
|[http://people.maths.ox.ac.uk/mackayj/ John Mackay] (Oxford University)<br />
|[[#John Mackay (Oxford University)|<br />
''What does a random group look like?'']]<br />
|[http://www.math.wisc.edu/~dymarz/ Tullia]<br />
|-<br />
|October 7<br />
|[http://mypage.iu.edu/~fisherdm/ David Fisher] (Indiana University)<br />
|[[#David Fisher (Indiana University)|<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard and Tullia]<br />
|-<br />
|October 14<br />
|[http://www.cpt.univ-mrs.fr/~lanneau/ Erwan Lanneau] (University of Marseille, CPT)<br />
|[[#Erwan Lanneau (University of Marseille, CPT)|<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction'']]<br />
|[http://www.math.wisc.edu/~jeanluc/ Jean Luc]<br />
|-<br />
|October 21<br />
|[http://www.math.wisc.edu/~rsong/ Ruifang Song] (UW Madison)<br />
|[[#Ruifang Song (UW Madison)|<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties'']]<br />
|[local]<br />
|-<br />
|October 24 ( with Geom. analysis seminar)<br />
|[http://math.univ-lyon1.fr/~ovsienko/ Valentin Ovsienko] (University of Lyon)<br />
|[[#Valentin Ovsienko (University of Lyon)|<br />
''The pentagram map and generalized friezes of Coxeter'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|November 4<br />
| Steven Simon (NYU)<br />
|[[#Steven Simon (NYU))|<br />
''Equivariant Analogues of the Ham Sandwich Theorem'']]<br />
|[http://www.math.wisc.edu/~maxim/ Max]<br />
|-<br />
|November 18<br />
|[http://www.math.tamu.edu/~zelenko/ Igor Zelenko] (Texas A&M University)<br />
|[[#Igor Zelenko (Texas A&M University)|<br />
''On geometry of curves of flags of constant type'']]<br />
|[http://www.math.wisc.edu/~maribeff/ Gloria]<br />
|-<br />
|December 1<br />
|<br />
|[[#Bing Wang (Simons Center for Geometry and Physics)<br />
''Uniformization of algebraic varieties'']]<br />
|[Jeff]<br />
|-<br />
|December 2<br />
|[http://www.math.uic.edu/~ddumas/ David Dumas] (University of Illinois at Chicago)<br />
|[[#David Dumas (University of Illinois at Chicago)|<br />
''Real and complex boundaries in the character variety'']]<br />
|[http://www.math.wisc.edu/~rkent/ Richard]<br />
|-<br />
|December 9<br />
|[http://math.stanford.edu/~bfclarke/home/Home.html Brian Clarke] (Stanford)<br />
|[[#Brian Clarke (Stanford)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Gloria Mari Beffa (UW Madison)===<br />
''The pentagram map and generalizations: discretizations of AGD flows''<br />
<br />
GIven an n-gon one can join every other vertex with a segment and find the intersection <br />
of two consecutive segments. We can form a new n-gon with these intersections, and the<br />
map taking the original n-gon to the newly found one is called the pentagram map. The map's<br />
properties when defined on pentagons are simple to describe (it takes its name from this fact),<br />
but the map turns out to have a unusual number of other properties and applications. <br />
<br />
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the<br />
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram<br />
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will<br />
NOT be for experts and will have plenty of drawings, so come and join us.<br />
<br />
===Ke Zhu (University of Minnesota)===<br />
''Thin instantons in G2-manifolds and <br />
Seiberg-Witten invariants''<br />
<br />
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$<br />
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.<br />
<br />
===Antonio Ache (UW Madison)===<br />
Obstruction-Flat Asymptotically Locally Euclidean Metrics<br />
<br />
Given an even dimensional Riemannian manifold <math>(M^{n},g)</math> with <math>n\ge 4</math>, it was shown in the work of Charles Fefferman and Robin Graham on conformal invariants the existence of a non-trivial 2-tensor which involves <math>n</math> derivatives of the metric, arises as the first variation of a conformally invariant and vanishes for metrics that are conformally Einstein. This tensor is called the Ambient Obstruction tensor and is a higher dimensional generalization of the Bach tensor in dimension 4. We show that any asymptotically locally Euclidean (ALE) metric which is obstruction flat and scalar-flat must be ALE of a certain optimal order using a technique developed by Cheeger and Tian for Ricci-flat metrics. We also show a singularity removal theorem for obstruction-flat metrics with isolated <math>C^{0}</math>-orbifold singularities. In addition, we show that our methods apply to more general systems. This is joint work with Jeff Viaclovsky.<br />
<br />
===John Mackay (Oxford University)===<br />
''What does a random group look like?''<br />
<br />
Twenty years ago, Gromov introduced his density model for random groups, and showed when the density parameter is less than one half a random group is, with overwhelming probability, (Gromov) hyperbolic. Just as the classical hyperbolic plane has a circle as its boundary at infinity, hyperbolic groups have a boundary at infinity which carries a<br />
canonical conformal structure.<br />
<br />
In this talk, I will survey some of what is known about random groups, and how the geometry of a hyperbolic group corresponds to the structure of its boundary at infinity. I will outline recent work showing how Pansu's conformal dimension, a variation on Hausdorff dimension, can be<br />
used to give a more refined geometric picture of random groups at small densities.<br />
<br />
===David Fisher (Indiana University)===<br />
''Hodge-de Rham theory for infinite dimensional bundles and local rigidity''<br />
<br />
It is well known that every cohomology class on a manifold<br />
can be represented by a harmonic form. While this fact continues to hold<br />
for cohomology with coefficients in finite dimensional vector bundles, it<br />
is also fairly well known that it fails for infinite dimensional bundles. In<br />
this talk, I will formulate a notion of a harmonic cochain in group cohomology<br />
and explain what piece of the cohomology can be represented by<br />
harmonic cochains.<br />
I will use these ideas to prove a vanishing theorem that motivates a family of<br />
generalizations of property (T) of Kazhdan. If time permits, I will<br />
discuss applications<br />
to local rigidity of group actions.<br />
<br />
===Erwan Lanneau (University of Marseille, CPT)===<br />
''Dilatations of pseudo-Anosov homeomorphisms and Rauzy-Veech induction''<br />
<br />
In this talk I will explain the link between pseudo-Anosov homeomorphisms and Rauzy-Veech induction. We will see how to derive properties on the dilatations of these homeomorphisms (I will recall the definitions) and as an application, we will use the Rauzy-Veech-Yoccoz induction to give lower bound on dilatations.<br />
This is a common work with Corentin Boissy (Marseille).<br />
<br />
<br />
===Ruifang Song (UW Madison)===<br />
''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties''<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus its solution space is finite dimensional assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. When X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which play important roles in studying periods of Calabi-Yau hypersurfaces in toric varieties. This is based on joint work with Bong Lian and Shing-Tung Yau.<br />
<br />
===Valentin Ovsienko (University of Lyon)===<br />
''The pentagram map and generalized friezes of Coxeter''<br />
<br />
The pentagram map is a discrete integrable system on the moduli space of n-gons in the projective plane (which is a close relative of the moduli space of genus 0 curves with n marked points). The most interesting properties of the pentagram map is its relations to the theory of cluster algebras and to the classical integrable systems (such as the Boussinesq equation). I will talk of the recent results proving the integrability as well as of the algebraic and arithmetic properties of the pentagram map.<br />
In particular, I will introduce the space of 2-frieze patterns generalizing that of the classical Coxeter friezes and define the structure of cluster manifold on this space. The talk is based on joint works with Sophie Morier-Genoud, Richard Schwartz and Serge Tabachnikov.<br />
<br />
===Steven Simon (NYU)===<br />
''Equivariant Analogues of the Ham Sandwich Theorem''<br />
<br />
The Ham Sandwich Theorem, one of the earliest applications of algebraic topology to geometric combinatorics, states that under generic conditions any n finite Borel measures on R^n can be bisected by a single hyperplane. Viewing this theorem as a Z_2-symmetry statement for measures, we generalize the theorem to other finite groups, notably the finite subgroups of the spheres S^1 and S^3, in each case realizing group symmetry on Euclidian space as group symmetries of its Borel measures by studying the topology of associated spherical space forms. Direct equipartition statements for measures are given as special cases. We shall also discuss the contributions of the tangent bundles of these manifolds in answering similar questions. <br />
<br />
===Igor Zelenko (Texas A&M University)===<br />
''On geometry of curves of flags of constant type''<br />
<br />
The talk is devoted to the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for such problem. Under some natural assumptions on the subgroup $G$ and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure Linear Algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves.<br />
<br />
Our motivation to study such equivalence problems comes from the new approach to the geometry of structures of nonholonomic nature on manifolds such as vector distributions, sub-Riemannian structure etc. This approach is based on the Optimal Control Theory and it consists of the reduction of the equivalence problem for such nonholonomic geometric structures to the (extrinsic) differential geometry of curves in Lagrangian Grassmannians and, more generally, of curves of flags of isotropic and coisotropic subspaces in a linear symplectic space with respect to the action of the Linear Symplectic Group. The application of the general theory to the geometry of such curves case will be discussed in more detail.<br />
<br />
===David Dumas (University of Illinois at Chicago)===<br />
''Real and complex boundaries in the character variety''<br />
<br />
The set of holonomy representations of complex projective structures<br />
on a compact Riemann surface is a submanifold of the SL(2,C) character<br />
variety of the fundamental group. We will discuss the real- and<br />
complex-analytic geometry of this manifold and its interaction with<br />
the Morgan-Shalen compactification of the character variety. In<br />
particular we show that the subset consisting of holonomy<br />
representations that extend over a given hyperbolic 3-manifold group<br />
(of which the surface is an incompressible boundary) is discrete.<br />
<br />
===Brian Clarke (Stanford)===<br />
''TBA''<br />
<br />
<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=1556Geometry and Topology Seminar2011-01-28T19:57:35Z<p>Jeffv: /* Spring 2011 */</p>
<hr />
<div>== Spring 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
|Mohammed Abouzaid (Clay Institute & MIT)<br />
|[[#Mohammed Abouzaid (Clay Institute & MIT)|<br />
''A plethora of exotic Stein manifolds'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|February 4<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (UW-Madison)<br />
|[[#Laurentiu Maxim (UW-Madison)|<br />
''Intersection Space Homology and Hypersurface Singularities'']]<br />
|local<br />
|-<br />
|February 11<br />
|[http://www.math.wisc.edu/~rkent/ Richard Kent] (UW-Madison)<br />
|[[#Richard Kent (UW-Madison)|<br />
''Mapping class groups through profinite spectacles'']]<br />
|local<br />
|-<br />
|February 18<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff Viaclovsky] (UW-Madison)<br />
|[[#Jeff Viaclovsky (UW-Madison)|<br />
''Rigidity and stability of Einstein metrics for quadratic curvature functionals'']]<br />
|local<br />
|-<br />
|March 4<br />
|[http://www.massey.math.neu.edu/ David Massey] (Northeastern)<br />
|[[#David Massey (Northeastern)|<br />
''Lê Numbers and the Topology of Non-isolated Hypersurface Singularities'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|March 11<br />
|Danny Calegari (Cal Tech)<br />
|[[#Danny Calegari (Cal Tech)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|'''March 23, Wed, Room: TBA'''<br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|[[#Joerg Schuermann (University of Muenster, Germany)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|April 4<br />
|[http://euclid.colorado.edu/~gwilkin/ Graeme Wilkin] (U of Colorado-Boulder)<br />
|[[#Graeme Wilkin (U of Colorado-Boulder)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~mehrotra/ Sukhendu]<br />
|-<br />
|May 6<br />
|[http://www.math.neu.edu/~suciu/ Alex Suciu] (Northeastern)<br />
|[[#Alex Suciu (Northeastern)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|May 13<br />
|[http://www.math.wustl.edu/~apelayo/ Alvaro Pelayo] (IAS)<br />
|[[#Alvaro Pelayo (IAS)|<br />
''Symplectic Dynamics of integrable Hamiltonian systems'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Mohammed Abouzaid (Clay Institute & MIT)===<br />
''A plethora of exotic Stein manifolds''<br />
<br />
In real dimensions greater than 4, I will explain how a smooth <br />
manifold underlying an affine variety admits uncountably many distinct<br />
(Wein)stein structures, of which countably many have finite type,<br />
and which are distinguished by their symplectic cohomology groups.<br />
Starting with a Lefschetz fibration on such a variety, I shall per-<br />
form an explicit sequence of appropriate surgeries, keeping track of<br />
the changes to the Fukaya category and hence, by understanding<br />
open-closed maps, obtain descriptions of symplectic cohomology af-<br />
ter surgery. (joint work with P. Seidel)<br />
<br />
===Laurentiu Maxim (UW-Madison)===<br />
''Intersection Space Homology and Hypersurface Singularities''<br />
<br />
A recent homotopy-theoretic procedure due to Banagl assigns to a certain singular space a cell complex, its intersection space, whose rational cohomology possesses Poincare duality. This yields a new cohomology theory for singular spaces, which has a richer internal algebraic structure than intersection cohomology (e.g., it has cup products), and which addresses certain questions in type II string theory related to massless D-branes arising during a Calabi-Yau conifold transition.<br />
<br />
While intersection cohomology is stable under small resolutions, in recent joint work with Markus Banagl we proved that the new theory is often stable under smooth deformations of hypersurface singularities. When this is the case, we showed that the rational cohomology of the intersection space can be endowed with a mixed Hodge structure compatible with Deligne's mixed Hodge structure on the ordinary cohomology of the singular hypersurface.<br />
<br />
===Richard Kent (UW-Madison)===<br />
''Mapping class groups through profinite spectacles''<br />
<br />
It is a theorem of Bass, Lazard, and Serre, and, independently,<br />
Mennicke, that the special linear group SL(n,Z) enjoys the congruence<br />
subgroup property when n is at least 3. This property is most quickly<br />
described by saying that the profinite completion of the special<br />
linear group injects into the special linear group of the profinite<br />
completion of Z. There is a natural analog of this property for<br />
mapping class groups of surfaces. Namely, one may ask if the<br />
profinite completion of the mapping class group embeds in the outer<br />
automorphism group of the profinite completion of the surface group.<br />
<br />
M. Boggi has a program to establish this property for mapping class<br />
groups. I'll discuss some partial results, and what remains to be<br />
done.<br />
<br />
===Jeff Viaclovsky (UW-Madison)===<br />
''Rigidity and stability of Einstein metrics for quadratic curvature functionals''<br />
<br />
===David Massey (Northeastern)===<br />
''Lê Numbers and the Topology of Non-isolated Hypersurface Singularities''<br />
<br />
The results of Milnor from his now-classic 1968 work "Singular Points of Complex Hypersurfaces" are particularly strong when the singular points are isolated. One of the most striking subsequent results in this area, was the 1976 result of Lê and Ramanujam, in which the h-Cobordism Theorem was used to prove that constant Milnor number implies constant topological-type, for families of isolated hypersurfaces.<br />
<br />
In this talk, I will discuss the Lê cycles and Lê numbers of a singular hypersurface, and the results which seem to indicate that they are the "correct" generalization of the Milnor number for non-isolated hypersurface singularities.<br />
<br />
===Danny Calegari (Cal Tech)===<br />
''TBA''<br />
<br />
===Graeme Wilkin (U of Colorado-Boulder)===<br />
''TBA''<br />
<br />
===Alex Suciu (Northeastern)===<br />
''TBA''<br />
<br />
===Joerg Schuermann (Muenster)===<br />
''TBA''<br />
<br />
===Alvaro Pelayo (IAS)===<br />
''Symplectic Dynamics of integrable Hamiltonian systems''<br />
<br />
I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic<br />
group action, and the classical structure theorems of Kostant, Atiyah,<br />
Guillemin-Sternberg and Delzant on Hamiltonian torus actions.<br />
Then I will state a structure theorem for general symplectic torus<br />
actions, and give an idea of its proof. In the second part of the talk<br />
I will introduce new symplectic invariants of completely integrable<br />
Hamiltonian systems in low dimensions, and explain how these invariants<br />
determine, up to isomorphisms, the so called "semitoric systems".<br />
Semitoric systems are Hamiltonian systems which lie somewhere between the more<br />
rigid toric systems and the usually complicated general integrable<br />
systems. Semitoric systems form a fundamental class of integrable systems,<br />
commonly found in simple physical models such as the coupled<br />
spin-oscillator, the Lagrange top and the spherical pendulum. Parts of<br />
this talk are based on joint work with with Johannes J. Duistermaat and<br />
San Vu Ngoc.<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffvhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=1555Geometry and Topology Seminar2011-01-28T19:56:53Z<p>Jeffv: /* Abstracts */</p>
<hr />
<div>== Spring 2011 ==<br />
<br />
The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
|Mohammed Abouzaid (Clay Institute & MIT)<br />
|[[#Mohammed Abouzaid (Clay Institute & MIT)|<br />
''A plethora of exotic Stein manifolds'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|February 4<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (UW-Madison)<br />
|[[#Laurentiu Maxim (UW-Madison)|<br />
''Intersection Space Homology and Hypersurface Singularities'']]<br />
|local<br />
|-<br />
|February 11<br />
|[http://www.math.wisc.edu/~rkent/ Richard Kent] (UW-Madison)<br />
|[[#Richard Kent (UW-Madison)|<br />
''Mapping class groups through profinite spectacles'']]<br />
|local<br />
|-<br />
|February 18<br />
|[http://www.math.wisc.edu/~jeffv/ Jeff Viaclovsky] (UW-Madison)<br />
|[[#Jeff Viaclovsky (UW-Madison)|<br />
''TBA'']]<br />
|local<br />
|-<br />
|March 4<br />
|[http://www.massey.math.neu.edu/ David Massey] (Northeastern)<br />
|[[#David Massey (Northeastern)|<br />
''Lê Numbers and the Topology of Non-isolated Hypersurface Singularities'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|March 11<br />
|Danny Calegari (Cal Tech)<br />
|[[#Danny Calegari (Cal Tech)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|'''March 23, Wed, Room: TBA'''<br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|[[#Joerg Schuermann (University of Muenster, Germany)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|April 4<br />
|[http://euclid.colorado.edu/~gwilkin/ Graeme Wilkin] (U of Colorado-Boulder)<br />
|[[#Graeme Wilkin (U of Colorado-Boulder)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~mehrotra/ Sukhendu]<br />
|-<br />
|May 6<br />
|[http://www.math.neu.edu/~suciu/ Alex Suciu] (Northeastern)<br />
|[[#Alex Suciu (Northeastern)|<br />
''TBA'']]<br />
|[http://www.math.wisc.edu/~maxim/ Maxim]<br />
|-<br />
|May 13<br />
|[http://www.math.wustl.edu/~apelayo/ Alvaro Pelayo] (IAS)<br />
|[[#Alvaro Pelayo (IAS)|<br />
''Symplectic Dynamics of integrable Hamiltonian systems'']]<br />
|[http://www.math.wisc.edu/~oh/ Yong-Geun]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Mohammed Abouzaid (Clay Institute & MIT)===<br />
''A plethora of exotic Stein manifolds''<br />
<br />
In real dimensions greater than 4, I will explain how a smooth <br />
manifold underlying an affine variety admits uncountably many distinct<br />
(Wein)stein structures, of which countably many have finite type,<br />
and which are distinguished by their symplectic cohomology groups.<br />
Starting with a Lefschetz fibration on such a variety, I shall per-<br />
form an explicit sequence of appropriate surgeries, keeping track of<br />
the changes to the Fukaya category and hence, by understanding<br />
open-closed maps, obtain descriptions of symplectic cohomology af-<br />
ter surgery. (joint work with P. Seidel)<br />
<br />
===Laurentiu Maxim (UW-Madison)===<br />
''Intersection Space Homology and Hypersurface Singularities''<br />
<br />
A recent homotopy-theoretic procedure due to Banagl assigns to a certain singular space a cell complex, its intersection space, whose rational cohomology possesses Poincare duality. This yields a new cohomology theory for singular spaces, which has a richer internal algebraic structure than intersection cohomology (e.g., it has cup products), and which addresses certain questions in type II string theory related to massless D-branes arising during a Calabi-Yau conifold transition.<br />
<br />
While intersection cohomology is stable under small resolutions, in recent joint work with Markus Banagl we proved that the new theory is often stable under smooth deformations of hypersurface singularities. When this is the case, we showed that the rational cohomology of the intersection space can be endowed with a mixed Hodge structure compatible with Deligne's mixed Hodge structure on the ordinary cohomology of the singular hypersurface.<br />
<br />
===Richard Kent (UW-Madison)===<br />
''Mapping class groups through profinite spectacles''<br />
<br />
It is a theorem of Bass, Lazard, and Serre, and, independently,<br />
Mennicke, that the special linear group SL(n,Z) enjoys the congruence<br />
subgroup property when n is at least 3. This property is most quickly<br />
described by saying that the profinite completion of the special<br />
linear group injects into the special linear group of the profinite<br />
completion of Z. There is a natural analog of this property for<br />
mapping class groups of surfaces. Namely, one may ask if the<br />
profinite completion of the mapping class group embeds in the outer<br />
automorphism group of the profinite completion of the surface group.<br />
<br />
M. Boggi has a program to establish this property for mapping class<br />
groups. I'll discuss some partial results, and what remains to be<br />
done.<br />
<br />
===Jeff Viaclovsky (UW-Madison)===<br />
''Rigidity and stability of Einstein metrics for quadratic curvature functionals''<br />
<br />
===David Massey (Northeastern)===<br />
''Lê Numbers and the Topology of Non-isolated Hypersurface Singularities''<br />
<br />
The results of Milnor from his now-classic 1968 work "Singular Points of Complex Hypersurfaces" are particularly strong when the singular points are isolated. One of the most striking subsequent results in this area, was the 1976 result of Lê and Ramanujam, in which the h-Cobordism Theorem was used to prove that constant Milnor number implies constant topological-type, for families of isolated hypersurfaces.<br />
<br />
In this talk, I will discuss the Lê cycles and Lê numbers of a singular hypersurface, and the results which seem to indicate that they are the "correct" generalization of the Milnor number for non-isolated hypersurface singularities.<br />
<br />
===Danny Calegari (Cal Tech)===<br />
''TBA''<br />
<br />
===Graeme Wilkin (U of Colorado-Boulder)===<br />
''TBA''<br />
<br />
===Alex Suciu (Northeastern)===<br />
''TBA''<br />
<br />
===Joerg Schuermann (Muenster)===<br />
''TBA''<br />
<br />
===Alvaro Pelayo (IAS)===<br />
''Symplectic Dynamics of integrable Hamiltonian systems''<br />
<br />
I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic<br />
group action, and the classical structure theorems of Kostant, Atiyah,<br />
Guillemin-Sternberg and Delzant on Hamiltonian torus actions.<br />
Then I will state a structure theorem for general symplectic torus<br />
actions, and give an idea of its proof. In the second part of the talk<br />
I will introduce new symplectic invariants of completely integrable<br />
Hamiltonian systems in low dimensions, and explain how these invariants<br />
determine, up to isomorphisms, the so called "semitoric systems".<br />
Semitoric systems are Hamiltonian systems which lie somewhere between the more<br />
rigid toric systems and the usually complicated general integrable<br />
systems. Semitoric systems form a fundamental class of integrable systems,<br />
commonly found in simple physical models such as the coupled<br />
spin-oscillator, the Lagrange top and the spherical pendulum. Parts of<br />
this talk are based on joint work with with Johannes J. Duistermaat and<br />
San Vu Ngoc.<br />
<br />
[[Fall-2010-Geometry-Topology]]</div>Jeffv