https://hilbert.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Feldman&feedformat=atomUW-Math Wiki - User contributions [en]2021-04-16T20:47:21ZUser contributionsMediaWiki 1.30.1https://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18952PDE Geometric Analysis seminar2020-02-07T16:14:16Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Mathew Langford | Concavity of the arrival time ]]<br />
| Angenent<br />
|- <br />
|Dec 9 - Colloquium (4-5PM)<br />
| Hui Yu (Columbia)<br />
|[[#Hui Yu | TBA ]]<br />
| Tran<br />
|- <br />
|Feb. 3<br />
| Philippe LeFloch (Sorbonne University and CNRS)<br />
|[[#Philippe LeFloch | Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions ]]<br />
| Feldman<br />
|- <br />
|Feb. 10<br />
| Joonhyun La (Stanford)<br />
|[[#Joonhyun La | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| organizer<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 20<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.<br />
<br />
===Mathew Langford===<br />
Title: Concavity of the arrival time<br />
<br />
Abstract: We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a novel concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton’s differential Harnack inequality for mean curvature flow and, more generally, Andrews’ differential Harnack inequalities for certain “$\alpha$-inverse-concave” flows.<br />
<br />
===Philippe LeFloch===<br />
Title: Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions<br />
<br />
Abstract: I will present recent progress on the global evolution problem for self-gravitating matter. (1) For Einstein's constraint equations, motivated by a scheme proposed by Carlotto and Schoen I will show the existence of asymptotically Euclidean Einstein spaces with low decay; joint work with T. Nguyen. <br />
<br />
(2) For Einstein's evolution equations in the regime near Minkowski spacetime, I will show the global nonlinear stability of massive matter fields; joint work with Y. Ma. <br />
<br />
(3) For the colliding gravitational wave problem, I will show the existence of weakly regular spacetimes containing geometric singularities across which junction conditions are imposed; joint work with B. Le Floch and G. Veneziano.<br />
<br />
<br />
===Joonhyun La===<br />
Title: On a kinetic model of polymeric fluids<br />
<br />
Abstract: In this talk, we prove global well-posedness of a system describing behavior of dilute flexible polymeric fluids. This model is based on kinetic theory, and a main difficulty for this system is its multi-scale nature. A new function space, based on moments, is introduced to address this issue, and this function space allows us to deal with larger initial data.<br />
<br />
===Adrian Tudorascu===<br />
Title: On the Lagrangian description of the Sticky Particle flow <br />
<br />
Abstract: R. Hynd has recently proved that for absolutely continuous initial velocities the Sticky Particle system admits solutions described by monotone flow maps in Lagrangian coordinates. We present a generalization of this result to general initial velocities and discuss some consequences. (This is based on ongoing work with M. Suder.)</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18740PDE Geometric Analysis seminar2020-01-22T19:22:33Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Mathew Langford | Concavity of the arrival time ]]<br />
| Angenent<br />
|- <br />
|Dec 9 - Colloquium (4-5PM)<br />
| Hui Yu (Columbia)<br />
|[[#Hui Yu | TBA ]]<br />
| Tran<br />
|- <br />
|Feb. 3<br />
| Philippe LeFloch (Sorbonne University and CNRS)<br />
|[[#Philippe LeFloch | Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions ]]<br />
| Feldman<br />
|- <br />
|Feb. 10<br />
| Joonhyun La (Stanford)<br />
|[[#Joonhyun La | TBA ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| organizer<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 20<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.<br />
<br />
===Mathew Langford===<br />
Title: Concavity of the arrival time<br />
<br />
Abstract: We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a novel concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton’s differential Harnack inequality for mean curvature flow and, more generally, Andrews’ differential Harnack inequalities for certain “$\alpha$-inverse-concave” flows.<br />
<br />
===Philippe LeFloch===<br />
Title: Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions<br />
<br />
Abstract: I will present recent progress on the global evolution problem for self-gravitating matter. (1) For Einstein's constraint equations, motivated by a scheme proposed by Carlotto and Schoen I will show the existence of asymptotically Euclidean Einstein spaces with low decay; joint work with T. Nguyen. <br />
<br />
(2) For Einstein's evolution equations in the regime near Minkowski spacetime, I will show the global nonlinear stability of massive matter fields; joint work with Y. Ma. <br />
<br />
(3) For the colliding gravitational wave problem, I will show the existence of weakly regular spacetimes containing geometric singularities across which junction conditions are imposed; joint work with B. Le Floch and G. Veneziano.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18737PDE Geometric Analysis seminar2020-01-22T19:11:12Z<p>Feldman: /* PDE GA Seminar Schedule Fall 2019-Spring 2020 */</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 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Mathew Langford | Concavity of the arrival time ]]<br />
| Angenent<br />
|- <br />
|Dec 9 - Colloquium (4-5PM)<br />
| Hui Yu (Columbia)<br />
|[[#Hui Yu | TBA ]]<br />
| Tran<br />
|- <br />
|Feb. 3<br />
| Philippe LeFloch (Sorbonne University and CNRS)<br />
|[[#Philippe LeFloch | Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions ]]<br />
| Feldman<br />
|- <br />
|Feb. 10<br />
| Joonhyun La (Stanford)<br />
|[[#Joonhyun La | TBA ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| organizer<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 20<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.<br />
<br />
===Mathew Langford===<br />
Title: Concavity of the arrival time<br />
<br />
Abstract: We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a novel concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton’s differential Harnack inequality for mean curvature flow and, more generally, Andrews’ differential Harnack inequalities for certain “$\alpha$-inverse-concave” flows.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18443PDE Geometric Analysis seminar2019-11-18T06:10:25Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|Feb. 3<br />
| Philippe LeFloch (Sorbonne Université)<br />
|[[#Speaker | TBA ]]<br />
| Feldman<br />
|- <br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| organizer<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 20<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18424PDE Geometric Analysis seminar2019-11-15T21:44:45Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|Feb. 3<br />
| TBA<br />
|[[#Speaker | TBA ]]<br />
| Feldman<br />
|- <br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| organizer<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 20<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18289PDE Geometric Analysis seminar2019-11-01T22:01:53Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Nov 11<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 20<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17236PDE Geometric Analysis seminar2019-03-29T16:14:41Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3, ''' Time: 3:00, Room: B223 Van Vleck '''<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | Flocking Models with Singular Interaction Kernels ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''<br />
|Serena Federico (MIT)<br />
|[[#Serena Federico | Sufficient conditions for local solvability of some degenerate partial differential operators ]]<br />
| Mihaela Ifrim <br />
|- <br />
|December 10, Colloquium, '''Time: 4:00''' <br />
| [https://math.mit.edu/~maxe/ Max Engelstein] (MIT)<br />
|[[#Max Engelstein| The role of Energy in Regularity ]]<br />
| Feldman<br />
|- <br />
|January 28,<br />
| Ru-Yu Lai (Minnesota)<br />
|[[#Ru-Yu Lai | Inverse transport theory and related applications ]]<br />
| Li and Kim <br />
|-<br />
| February 4,<br />
|<br />
|[[# | No seminar (several relevant colloquiums in Feb/5 and Feb/8)]]<br />
| <br />
|-<br />
| February 11,<br />
| Seokbae Yun (SKKU, long term visitor of UW-Madison)<br />
|[[# Seokbae Yun | The propagations of uniform upper bounds fo the spatially homogeneous relativistic Boltzmann equation]]<br />
| Kim <br />
|-<br />
| February 13 '''4PM''',<br />
| Dean Baskin (Texas A&M)<br />
|[[#Dean Baskin | Radiation fields for wave equations]]<br />
| Colloquium<br />
|- <br />
| February 18, '''3:30PM, Room: VV B239'''<br />
| Daniel Tataru (Berkeley)<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| Ifrim <br />
|- <br />
| February 19, '''Time: 4-5PM, Room: VV B139'''<br />
| Wenjia Jing (Tsinghua University)<br />
|[[#Wenjia Jing | Periodic homogenization of Dirichlet problems in perforated domains: a unified proof ]]<br />
| Tran<br />
|- <br />
|February 25,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | Quantitative homogenization in a balanced random environment ]]<br />
| Kim and Tran<br />
|-<br />
|March 4 '''time:4PM-5PM, Room: VV B239'''<br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | Stability of vacuum for the Landau equation with moderately soft potentials ]]<br />
| Kim<br />
|-<br />
|March 12, '''4:00 p.m. in VV B139'''<br />
| Trevor Leslie (UW-Madison)<br />
|[[# Trevor Leslie| TBA ]]<br />
| Analysis seminar<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|-<br />
|March 25<br />
| Jiaxin Jin<br />
|[[# Jiaxin Jin |Convergence to the complex balanced equilibrium for some reaction-diffusion systems with boundary equilibria. ]]<br />
| local speaker<br />
|- <br />
|April 1 <br />
| Zaher Hani (Michigan)<br />
|[[#Zaher Hani | TBA ]]<br />
| Ifrim<br />
|- <br />
|April 8 <br />
| Jingrui Cheng (Stony Brook) <br />
|[[#Jingrui Cheng | Gradient estimate for complex Monge-Ampere equations ]]<br />
| Feldman<br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 22,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| Beomjun Choi (Columbia)<br />
|[[#Beomjun Choi | Evolution of non-compact hypersurfaces by inverse mean curvature]]<br />
| Angenent<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.<br />
<br />
===Trevor Leslie===<br />
<br />
Title: Flocking Models with Singular Interaction Kernels<br />
<br />
Abstract: Many biological systems exhibit the property of self-organization, the defining feature of which is coherent, large-scale motion arising from underlying short-range interactions between the agents that make up the system. In this talk, we give an overview of some simple models that have been used to describe the so-called flocking phenomenon. Within the family of models that we consider (of which the Cucker-Smale model is the canonical example), writing down the relevant set of equations amounts to choosing a kernel that governs the interaction between agents. We focus on the recent line of research that treats the case where the interaction kernel is singular. In particular, we discuss some new results on the wellposedness and long-time dynamics of the Euler Alignment model and the Shvydkoy-Tadmor model.<br />
<br />
===Serena Federico===<br />
<br />
Title: Sufficient conditions for local solvability of some degenerate partial differential operators <br />
<br />
Abstract: In this talk we will give sufficient conditions for the local solvability of a class of degenerate second order linear partial differential operators with smooth coefficients. The class under consideration, inspired by some generalizations of the Kannai operator, is characterized by the presence of a complex subprincipal symbol. By giving suitable conditions on the subprincipal part and using the technique of a priori estimates, we will show that the operators in the class are at least $L^2$ to $L^2$ locally solvable.<br />
<br />
===Max Engelstein===<br />
<br />
Title: The role of Energy in Regularity<br />
<br />
Abstract: The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.<br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.<br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur.<br />
<br />
<br />
===Ru-Yu Lai===<br />
Title: Inverse transport theory and related applications.<br />
<br />
Abstract: The inverse transport problem consists of reconstructing the optical properties of a medium from boundary measurements. It finds applications in a variety of fields. In particular, radiative transfer equation (a linear transport equation) models the photon propagation in a medium in optical tomography. In this talk we will address results on the determination of these optical parameters. Moreover, the connection between the inverse transport problem and the Calderon problem will also be discussed.<br />
<br />
===Seokbae Yun===<br />
Title: The propagations of uniform upper bounds fo the spatially homogeneous relativistic Boltzmann equation<br />
<br />
Abstract: In this talk, we consider the propagation of the uniform upper bounds<br />
for the spatially homogenous relativistic Boltzmann equation. For this, we establish two<br />
types of estimates for the the gain part of the collision operator: namely, a potential<br />
type estimate and a relativistic hyper-surface integral estimate. We then combine them<br />
using the relativistic counter-part of the Carlemann representation to derive a uniform<br />
control of the gain part, which gives the desired propagation of the uniform bounds of<br />
the solution. Some applications of the results are also considered. This is a joint work <br />
with Jin Woo Jang and Robert M. Strain.<br />
<br />
<br />
<br />
===Daniel Tataru===<br />
<br />
Title: A Morawetz inequality for water waves.<br />
<br />
Authors: Thomas Alazard, Mihaela Ifrim, Daniel Tataru.<br />
<br />
Abstract: We consider gravity water waves in two space dimensions, with finite or infinite depth. Assuming some uniform scale invariant Sobolev bounds for the solutions, we prove local energy decay (Morawetz) estimates globally in time. Our result is uniform in the infinite depth limit. <br />
<br />
<br />
===Wenjia Jing===<br />
<br />
Title: Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
<br />
Abstract: In this talk, we present a unified proof to establish periodic homogenization for the Dirichlet problems associated to the Laplace operator in perforated domains; here the uniformity is with respect to the ratio between scaling factors of the perforation holes and the periodicity. Our method recovers, for critical scaling of the hole-cell ratio, the “strange term coming from nowhere” found by Cioranescu and Murat, and it works at the same time for other settings of hole-cell ratios. Moreover, the method is naturally based on analysis of rescaled cell problems and hence reveals the intrinsic connections among the apparently different homogenization behaviors in those different settings. We also show how to quantify the approach to get error estimates and corrector results.<br />
<br />
<br />
===Xiaoqin Guo===<br />
<br />
Title: Quantitative homogenization in a balanced random environment<br />
<br />
Abstract: Stochastic homogenization of discrete difference operators is closely related to the convergence of random walk in a random environment (RWRE) to its limiting process. In this talk we discuss non-divergence form difference operators in an i.i.d random environment and the corresponding process—a random walk in a balanced random environment in the integer lattice Z^d. We first quantify the ergodicity of the environment viewed from the point of view of the particle. As consequences, we obtain algebraic rates of convergence for the quenched central limit theorem of the RWRE and for the homogenization of both elliptic and parabolic non-divergence form difference operators. Joint work with J. Peterson (Purdue) and H. V. Tran (UW-Madison). <br />
<br />
===Sverak===<br />
<br />
Title: PDE aspects of the Navier-Stokes equations and simpler models<br />
<br />
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.<br />
<br />
===Jonathan Luk===<br />
<br />
Title: Stability of vacuum for the Landau equation with moderately soft potentials<br />
<br />
Abstract: Consider the Landau equation with moderately soft potentials in the whole space. We prove that sufficiently small and localized regular initial data give rise to unique global-in-time smooth solutions. Moreover, the solutions approach that of the free transport equation as $t\to +\infty$. This is the first stability of vacuum result for a binary collisional kinetic model featuring a long-range interaction.<br />
<br />
<br />
===Jiaxin Jin===<br />
<br />
Title: Convergence to the complex balanced equilibrium for some reaction-diffusion systems with boundary equilibria.<br />
<br />
Abstract: We first analyze a three-species system with boundary equilibria in some stoichiometric classes and study the rate of convergence to the complex balanced equilibrium. Then we prove similar results on the convergence to the positive equilibrium for a fairly general two-species reversible reaction-diffusion network with boundary equilibria.<br />
<br />
===Jingrui Cheng===<br />
<br />
Title: Gradient estimate for complex Monge-Ampere equations<br />
<br />
Abstract: We consider complex Monge-Ampere equations on a compact Kahler manifold. Previous gradient estimates of the solution all require some derivative bound of the right hand side. I will talk about how to get gradient estimate in $L^p$ and $L^{\infty}$, depending only on the continuity of the right hand side.<br />
<br />
<br />
<br />
===Beomjun Choi===<br />
In this talk, we first introduce the inverse mean curvature flow and its well known application in the the proof of Riemannian Penrose inequality by Huisken and Ilmanen. Then our main result on the existence and behavior of convex non-compact solution will be discussed. <br />
<br />
The key ingredient is a priori interior in time estimate on the inverse mean curvature in terms of the aperture of supporting cone at infinity. This is a joint work with P. Daskalopoulos and I will also mention the recent work with P.-K. Hung concerning the evolution of singular hypersurfaces.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16686Colloquia/Spring20192019-01-23T03:49:22Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
|[[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16668Colloquia/Spring20192019-01-21T22:18:21Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
|[[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16667Colloquia/Spring20192019-01-21T22:15:12Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
|[[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] ( Texas A&M)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16605Colloquia/Spring20192019-01-13T04:25:35Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] ( Texas A&M)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16568Colloquia/Spring20192018-12-17T17:06:30Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] ( Texas A&M)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16567Colloquia/Spring20192018-12-17T16:35:32Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] ( Texas A&M)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16566Colloquia/Spring20192018-12-17T16:29:14Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] ( Texas A&M)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| <br />
|[[# TBA| TBA ]]<br />
| <br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16527Colloquia/Fall182018-12-04T22:04:37Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| Surface bundles, monodromy, and arithmetic groups ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday, Room 911'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7 '''Room 911'''<br />
| [https://math.berkeley.edu/people/faculty/leonardo-zepeda-n-ez Leonardo Zepeda-Nunez](Berkeley)<br />
|[[#Dec 7: Leonardo Zepeda-Nunez (Berkeley) | Accelerating ab-initio molecular dynamics via multi-scale neural networks ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 3: Bena Tshishiku (Harvard) ===<br />
<br />
Surface bundles, monodromy, and arithmetic groups<br />
<br />
Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to ``compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. <br />
<br />
=== Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
=== Dec 7: Leonardo Zepeda-Nunez (Berkeley) ===<br />
<br />
Accelerating ab-initio molecular dynamics via multi-scale neural networks<br />
<br />
Deep learning has rapidly become a large field with an ever-growing range of applications; however, its intersection with scientific computing remains in its infancy, mainly due to the high accuracy that scientific computing problems require, which depends greatly on the architecture of the neural network. <br />
<br />
In this talk we present a novel deep neural network with a multi-scale architecture inspired in H-matrices (and H2-matrices) to efficiently approximate, within 3-4 digits, several challenging non-linear maps arising from the discretization of PDEs, whose evaluation would otherwise require computationally intensive iterative methods. <br />
<br />
In particular, we focus on the notoriously difficult Kohn-Sham map arising from Density Functional Theory (DFT). We show that the proposed multiscale-neural network can efficiently learn this map, thus bypassing an expensive self-consistent field iteration. In addition, we show the application of this methodology to ab-initio molecular dynamics, for which we provide examples for 1D problems and small, albeit realistic, 3D systems. <br />
<br />
Joint work with Y. Fan, J. Feliu-Faaba, L. Lin, W. Jia, and L. Ying<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16517Colloquia/Spring20192018-12-01T22:02:21Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)<br />
|[[# TBA| TBA ]]<br />
| Qin<br />
|<br />
|-<br />
|Feb 5 '''Tuesday'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[# TBA| TBA ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16502Colloquia/Fall182018-11-30T22:01:16Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| Surface bundles, monodromy, and arithmetic groups ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday, Room 911'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| [https://math.berkeley.edu/people/faculty/leonardo-zepeda-n-ez Leonardo Zepeda-Nunez](Berkeley)<br />
|[[#Dec 7: Leonardo Zepeda-Nunez (Berkeley) | Accelerating ab-initio molecular dynamics via multi-scale neural networks ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 3: Bena Tshishiku (Harvard) ===<br />
<br />
Surface bundles, monodromy, and arithmetic groups<br />
<br />
Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to ``compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. <br />
<br />
=== Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
=== Dec 7: Leonardo Zepeda-Nunez (Berkeley) ===<br />
<br />
Accelerating ab-initio molecular dynamics via multi-scale neural networks<br />
<br />
Deep learning has rapidly become a large field with an ever-growing range of applications; however, its intersection with scientific computing remains in its infancy, mainly due to the high accuracy that scientific computing problems require, which depends greatly on the architecture of the neural network. <br />
<br />
In this talk we present a novel deep neural network with a multi-scale architecture inspired in H-matrices (and H2-matrices) to efficiently approximate, within 3-4 digits, several challenging non-linear maps arising from the discretization of PDEs, whose evaluation would otherwise require computationally intensive iterative methods. <br />
<br />
In particular, we focus on the notoriously difficult Kohn-Sham map arising from Density Functional Theory (DFT). We show that the proposed multiscale-neural network can efficiently learn this map, thus bypassing an expensive self-consistent field iteration. In addition, we show the application of this methodology to ab-initio molecular dynamics, for which we provide examples for 1D problems and small, albeit realistic, 3D systems. <br />
<br />
Joint work with Y. Fan, J. Feliu-Faaba, L. Lin, W. Jia, and L. Ying<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16501Colloquia/Fall182018-11-30T21:59:28Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| Surface bundles, monodromy, and arithmetic groups ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday, Room 911'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| [https://math.berkeley.edu/people/faculty/leonardo-zepeda-n-ez Leonardo Zepeda-Nunez](Berkeley)<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | Accelerating ab-initio molecular dynamics via multi-scale neural networks ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 3: Bena Tshishiku (Harvard) ===<br />
<br />
Surface bundles, monodromy, and arithmetic groups<br />
<br />
Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to ``compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. <br />
<br />
=== Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
=== Dec 7: Leonardo Zepeda-Nunez ===<br />
<br />
Accelerating ab-initio molecular dynamics via multi-scale neural networks<br />
<br />
Deep learning has rapidly become a large field with an ever-growing range of applications; however, its intersection with scientific computing remains in its infancy, mainly due to the high accuracy that scientific computing problems require, which depends greatly on the architecture of the neural network. <br />
<br />
In this talk we present a novel deep neural network with a multi-scale architecture inspired in H-matrices (and H2-matrices) to efficiently approximate, within 3-4 digits, several challenging non-linear maps arising from the discretization of PDEs, whose evaluation would otherwise require computationally intensive iterative methods. <br />
<br />
In particular, we focus on the notoriously difficult Kohn-Sham map arising from Density Functional Theory (DFT). We show that the proposed multiscale-neural network can efficiently learn this map, thus bypassing an expensive self-consistent field iteration. In addition, we show the application of this methodology to ab-initio molecular dynamics, for which we provide examples for 1D problems and small, albeit realistic, 3D systems. <br />
<br />
Joint work with Y. Fan, J. Feliu-Faaba, L. Lin, W. Jia, and L. Ying<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16500Colloquia/Fall182018-11-30T21:57:32Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| Surface bundles, monodromy, and arithmetic groups ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday, Room 911'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| [https://math.berkeley.edu/people/faculty/leonardo-zepeda-n-ez Leonardo Zepeda-Nunez](Berkeley)<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | Accelerating ab-initio molecular dynamics via multi-scale neural networks ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 3: Bena Tshishiku (Harvard) ===<br />
<br />
Surface bundles, monodromy, and arithmetic groups<br />
<br />
Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to ``compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. <br />
<br />
=== Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
=== Dec 7: Leonardo Zepeda-Nunez ===<br />
<br />
Accelerating ab-initio molecular dynamics via multi-scale neural networks<br />
<br />
Deep learning has rapidly become a large field with an ever-growing range of applications; however, its intersection with scientific computing remains in its infancy, mainly due to the high accuracy that scientific computing problems require, which depends greatly on the architecture of the neural network. <br />
<br />
<br />
In this talk we present a novel deep neural network with a multi-scale architecture inspired in H-matrices (and H2-matrices) to efficiently approximate, within 3-4 digits, several challenging non-linear maps arising from the discretization of PDEs, whose evaluation would otherwise require computationally intensive iterative methods. <br />
<br />
<br />
In particular, we focus on the notoriously difficult Kohn-Sham map arising from Density Functional Theory (DFT). We show that the proposed multiscale-neural network can efficiently learn this map, thus bypassing an expensive self-consistent field iteration. In addition, we show the application of this methodology to ab-initio molecular dynamics, for which we provide examples for 1D problems and small, albeit realistic, 3D systems. <br />
<br />
<br />
Joint work with Y. Fan, J. Feliu-Faaba, L. Lin, W. Jia, and L. Ying<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16492Colloquia/Fall182018-11-30T04:40:26Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| Surface bundles, monodromy, and arithmetic groups ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday, Room 911'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 3: Bena Tshishiku (Harvard) ===<br />
<br />
Surface bundles, monodromy, and arithmetic groups<br />
<br />
Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to ``compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. <br />
<br />
=== Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16484Colloquia/Fall182018-11-29T05:47:36Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| Surface bundles, monodromy, and arithmetic groups ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 3: Bena Tshishiku (Harvard) ===<br />
<br />
Surface bundles, monodromy, and arithmetic groups<br />
<br />
Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to ``compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter. <br />
<br />
=== Dec 5: Subhabrata Sen (MIT and Microsoft Research New England) ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16482Colloquia/Fall182018-11-29T02:33:24Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| TBA ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen | Random graphs, Optimization, and Spin glasses ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 5: Subhabrata Sen ===<br />
<br />
Random graphs, Optimization, and Spin glasses<br />
<br />
Combinatorial optimization problems are ubiquitous in diverse mathematical applications. The desire to understand their ``typical" behavior motivates a study of these problems on random instances. In spite of a long and rich history, many natural questions in this domain are still intractable to rigorous mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection are canonical examples in this class. On the other hand, physicists study these questions using the non-rigorous ``replica" and ``cavity" methods, and predict complex, intriguing features. In this talk, I will describe some recent progress in our understanding of their typical properties on random graphs, obtained via connections to the theory of mean-field spin glasses. The new techniques are broadly applicable, and lead to novel algorithmic and statistical consequences.<br />
<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16462Colloquia/Fall182018-11-26T21:42:45Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| TBA ]]<br />
| Paul<br />
|<br />
|-<br />
|Dec 5 '''Wednesday'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT and Microsoft Research New England)<br />
|[[#Dec 5: Subhabrata Sen | TBA ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| Stechmann<br />
|<br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16461Colloquia/Fall182018-11-26T21:36:14Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| TBA ]]<br />
| <br />
|<br />
|-<br />
|Dec 5 '''Wednesday'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT)<br />
|[[#Dec 5: Subhabrata Sen | TBA ]]<br />
| <br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| <br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| The role of Energy in Regularity ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
=== Dec 10: Max Engelstein (MIT) ===<br />
<br />
The role of Energy in Regularity<br />
<br />
The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy. <br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field. <br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16453Colloquia/Fall182018-11-26T03:51:07Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher (Indiana U.) | New Techniques for Zimmer's Conjecture ]]<br />
| Kent<br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| TBA ]]<br />
| <br />
|<br />
|-<br />
|Dec 5 '''Wednesday'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT)<br />
|[[#Dec 5: Subhabrata Sen | TBA ]]<br />
| <br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| <br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| TBA ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
=== Nov 30: David Fisher (Indiana U.) ===<br />
<br />
New Techniques for Zimmer's Conjecture<br />
<br />
Lattices in higher rank simple Lie groups are known to be<br />
extremely rigid. Examples of this are Margulis' superrigidity theorem,<br />
which shows they have very few linear represenations, and Margulis'<br />
arithmeticity theorem, which shows they are all constructed via number<br />
theory. Motivated by these and other results, in 1983 Zimmer made a<br />
number of conjectures about actions of these groups on compact<br />
manifolds. After providing some history and motivation, I will discuss<br />
a recent result that makes dramatic progress on the conjecture in all<br />
cases and proves it in many of them. I will place some emphasis on<br />
surprising connections to other areas of mathematics that arise in the<br />
proof.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=16452PDE Geometric Analysis seminar2018-11-25T23:38:05Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3, ''' Time: 3:00, Room: B223 Van Vleck '''<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | Flocking Models with Singular Interaction Kernels ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''<br />
|Serena Federico (MIT)<br />
|[[#Serena Federico | TBA ]]<br />
| Mihaela Ifrim <br />
|- <br />
|December 10, Colloquium, '''Time: 4:00''' <br />
| Max Engelstein (MIT)<br />
|[[# | TBA ]]<br />
| Feldman<br />
|- <br />
|January 28,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|-<br />
|Time: TBD in February,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|Time: TBD in February,<br />
| Wenjia Jing (Tsinghua University)<br />
|[[#Wenjia Jing | TBA ]]<br />
| Tran<br />
|-<br />
|Time: TBD,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|March 4 <br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | TBA ]]<br />
| Kim<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.<br />
<br />
===Trevor Leslie===<br />
<br />
Title: Flocking Models with Singular Interaction Kernels<br />
<br />
Abstract: Many biological systems exhibit the property of self-organization, the defining feature of which is coherent, large-scale motion arising from underlying short-range interactions between the agents that make up the system. In this talk, we give an overview of some simple models that have been used to describe the so-called flocking phenomenon. Within the family of models that we consider (of which the Cucker-Smale model is the canonical example), writing down the relevant set of equations amounts to choosing a kernel that governs the interaction between agents. We focus on the recent line of research that treats the case where the interaction kernel is singular. In particular, we discuss some new results on the wellposedness and long-time dynamics of the Euler Alignment model and the Shvydkoy-Tadmor model.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16451Colloquia/Fall182018-11-25T23:29:12Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher(Indiana U.) | TBA ]]<br />
| <br />
|-<br />
|Dec 3 '''Monday'''<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku](Harvard)<br />
|[[#Dec 3: Bena Tshishiku (Harvard)| TBA ]]<br />
| <br />
|<br />
|-<br />
|Dec 5 '''Wednesday'''<br />
| [http://www.mit.edu/~ssen90/ Subhabrata Sen](MIT)<br />
|[[#Dec 5: Subhabrata Sen | TBA ]]<br />
| <br />
|<br />
|-<br />
|Dec 7<br />
| Leonardo Zepeda-Nunez<br />
|[[#Dec 7: Leonardo Zepeda-Nunez | TBA ]]<br />
| <br />
|-<br />
|Dec 10 '''Monday'''<br />
| [http://math.mit.edu/~maxe/ Max Engelstein](MIT)<br />
|[[#Dec 10: Max Engelstein (MIT)| TBA ]]<br />
| Feldman<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16450Colloquia/Fall182018-11-25T21:48:24Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | A Torelli type theorem ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher(Indiana U.) | TBA ]]<br />
| <br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
=== Nov 28: Gao Chen (IAS) ===<br />
<br />
A Torelli type theorem<br />
<br />
The length of a circle determines the shape of it. In this talk, we will discuss non-trivial generalizations of this fact for Riemann surfaces, hyperkähler 4-manifolds, Calabi-Yau threefolds and G_2, Spin(7) manifolds. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16449Colloquia/Fall182018-11-25T20:32:55Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Nov 28 '''Wednesday'''<br />
| [http://www.math.ias.edu/~gchen/ Gao Chen](IAS)<br />
|[[#Nov 28: Gao Chen(IAS) | TBA ]]<br />
| Paul <br />
|<br />
|-<br />
|Nov 30<br />
| [https://math.indiana.edu/about/faculty/fisher-david.html David Fisher](Indiana U.)<br />
|[[#Nov 30: David Fisher(Indiana U.) | TBA ]]<br />
| <br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16433Colloquia/Fall182018-11-20T21:56:01Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16432Colloquia/Fall182018-11-20T21:55:02Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 26 '''Monday, Room 911'''<br />
| [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin] (MIT)<br />
|[[#Nov 26: Vadim Gorin (MIT)| Macroscopic fluctuations through Schur generating functions ]]<br />
| Anderson<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
<br />
=== Nov 26: Vadim Gorin (MIT)===<br />
<br />
Macroscopic fluctuations through Schur generating functions<br />
<br />
I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.<br />
<br />
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16427Colloquia/Fall182018-11-20T02:58:45Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday, Room 911'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=16414PDE Geometric Analysis seminar2018-11-15T16:07:08Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3,<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | TBA ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''<br />
|Serena Federico (MIT)<br />
|[[#Serena Federico | TBA ]]<br />
| Mihaela Ifrim <br />
|- <br />
|January 28,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|-<br />
|Time: TBD in February,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|Time: TBD,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|March 4 <br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | TBA ]]<br />
| Kim<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=16413PDE Geometric Analysis seminar2018-11-15T15:58:39Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3,<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | TBA ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''<br />
|Serena Frederico (MIT)<br />
|[[#Serena Frederico | TBA ]]<br />
| Mihaela Ifrim <br />
|- <br />
|January 28,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|-<br />
|Time: TBD in February,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|Time: TBD,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|March 4 <br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | TBA ]]<br />
| Kim<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=16412PDE Geometric Analysis seminar2018-11-15T15:53:43Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3,<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | TBA ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, 2:25, Room: B223 Van Vleck <br />
|Serena Frederico (MIT)<br />
|[[#Serena Frederico | TBA ]]<br />
| Mihaela Ifrim <br />
|- <br />
|January 28,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|-<br />
|Time: TBD in February,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|Time: TBD,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|March 4 <br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | TBA ]]<br />
| Kim<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| ( )<br />
|[[# | TBA ]]<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16408Colloquia/Fall182018-11-14T21:34:53Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 20 '''Tuesday'''<br />
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)<br />
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)| Computability and Ramsey Theory ]]<br />
| Andrews<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
From analysis to algebra to geometry - an example in representation theory of real groups<br />
<br />
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).<br />
<br />
=== Nov 20: Denis Hirschfeldt (University of Chicago)===<br />
<br />
Computability and Ramsey Theory<br />
<br />
Computability theory can be seen as the study of the fine <br />
structure of definability. Much of its power relies on the deep <br />
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that <br />
computability-theoretically natural notions tend to be combinatorially <br />
natural, and vice-versa. I will discuss some results and open questions in <br />
the computability-theoretic analysis of combinatorial principles, in <br />
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16404Colloquia/Fall182018-11-14T17:54:51Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 19 '''Monday'''<br />
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech) <br />
|[[#Nov 19: Alexander Yom Din (Caltech) | Passing from analysis to algebra to geometry - an example in representation theory of real groups ]]<br />
| Boston, Gurevitch<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
=== Nov 19: Alexander Yom Din (Caltech)===<br />
<br />
Passing from analysis to algebra to geometry - an example in representation theory of real groups <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16365Colloquia/Fall182018-11-09T17:40:05Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2 '''Room 911'''<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 12 '''Monday'''<br />
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)<br />
|[[#Nov 9: Anne Shiu (Texas A&M) | Dynamics of biochemical reaction systems ]]<br />
| Craciun, Stechmann<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
=== Nov 9: Anne Shiu (Texas A&M)===<br />
<br />
Dynamics of biochemical reaction systems<br />
<br />
Reaction networks taken with mass-action kinetics arise in many settings, <br />
from epidemiology to population biology to systems of chemical reactions. <br />
This talk focuses on certain biological signaling networks, namely, <br />
phosphorylation networks, and their resulting dynamical systems. For many <br />
of these systems, the set of steady states admits a rational <br />
parametrization (that is, the set is the image of a map with <br />
rational-function coordinates). We describe how such a parametrization <br />
allows us to investigate the dynamics, including the emergence of <br />
bistability in a network underlying ERK regulation, and the capacity for <br />
oscillations in a mixed processive/distributive phosphorylation network.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16298Colloquia/Fall182018-10-29T16:34:51Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)<br />
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)<br />
|[[#Nov 2: Ruixiang Zhang (Madison) | The Fourier extension operator ]]<br />
| <br />
|<br />
|-<br />
|Nov 7 '''Wednesday'''<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT)| (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 12: Andrei Caldararu (Madison)===<br />
<br />
Mirror symmetry and derived categories<br />
<br />
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.<br />
<br />
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
=== Oct 26: Douglas Ulmer (Arizona)===<br />
<br />
Rational numbers, rational functions, and rational points<br />
<br />
One of the central concerns of arithmetic geometry is the study of<br />
solutions of systems of polynomial equations where the solutions are<br />
required to lie in a "small" field such as the rational numbers. I<br />
will explain the landscape of expectations and conjectures in this<br />
area, focusing on curves and their Jacobians over global fields<br />
(number fields and function fields), and then survey the progress made<br />
over the last decade in the function field case. The talk is intended<br />
to be accessible to a wide audience.<br />
<br />
=== Nov 2: Ruixiang Zhang (Madison)===<br />
<br />
The Fourier extension operator<br />
<br />
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.<br />
<br />
=== Nov 7: Luca Spolaor (MIT)===<br />
<br />
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems<br />
<br />
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.<br />
Finally I will describe some future applications of this method both in regularity theory and in other settings.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16159Colloquia/Fall182018-10-07T18:53:38Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)<br />
|[[# TBA| TBA ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16158Colloquia/Fall182018-10-05T19:55:06Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| ...<br />
|[[# TBA| TBA ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16157Colloquia/Fall182018-10-05T19:52:43Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| ...<br />
|[[# TBA| TBA ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[#Oct 19: Jeremy Teitelbaum (U Connecticut)| Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
=== Oct 19: Jeremy Teitelbaum (U Connecticut)===<br />
Lessons Learned and New Perspectives:<br />
From Dean and Provost to aspiring Data Scientist<br />
<br />
After more than 10 years in administration, including 9 as Dean of<br />
Arts and Sciences and 1 as interim Provost at UConn, I have returned<br />
to my faculty position. I am spending a year as a visiting scientist<br />
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,<br />
Connecticut, trying to get a grip on some of the mathematical problems<br />
of interest to researchers in cancer genomics. In this talk, I will offer some personal<br />
observations about being a mathematician and a high-level administrator, talk a bit about<br />
the research environment at an independent research institute like JAX-GM, outline<br />
a few problems that I've begun to learn about, and conclude with a<br />
discussion of how these experiences have shaped my view of graduate training in mathematics.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15559Colloquia/Fall182018-06-18T06:48:05Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12, 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguish Lecture series<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 5<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 12<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 2<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Blank&diff=15448Colloquia/Blank2018-04-20T15:19:20Z<p>Feldman: </p>
<hr />
<div><br />
== semester==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gunther Uhlmann (Univ. of Washington)<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT></div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Blank&diff=15447Colloquia/Blank2018-04-20T15:14:16Z<p>Feldman: </p>
<hr />
<div><br />
== semester==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 21, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gunther Uhlmann (Univ. of Washington)<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota)<br />
|[[# TBA| Wasow lecture ]]<br />
| Kim<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT></div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Blank&diff=15446Colloquia/Blank2018-04-20T15:11:39Z<p>Feldman: </p>
<hr />
<div><br />
== semester==<br />
<br />
{| cellpadding="8"<br />
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!align="left" | title<br />
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|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gunther Uhlmann (Univ. of Washington)<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
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|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota)<br />
|[[# TBA| Wasow lecture ]]<br />
| Kim<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT></div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=15433PDE Geometric Analysis seminar2018-04-19T00:34:20Z<p>Feldman: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2018 | Tentative schedule for Fall 2018]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Spring 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
<br />
|- <br />
|January 29, '''3-3:50PM, B341 VV.'''<br />
| Dan Knopf (UT Austin)<br />
|[[#Dan Knopf | Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons]]<br />
| Angenent<br />
|- <br />
|February 5, '''3-3:50PM, B341 VV.'''<br />
| Andreas Seeger (UW)<br />
|[[#Andreas Seeger | Singular integrals and a problem on mixing flows ]]<br />
| Kim & Tran<br />
|- <br />
|February 12<br />
| Sam Krupa (UT-Austin)<br />
|[[#Sam Krupa | Proving Uniqueness of Solutions for Burgers Equation Entropic for a Single Entropy, with Eye Towards Systems Case ]]<br />
| Lee <br />
|- <br />
|February 19<br />
| Maja Taskovic (UPenn)<br />
|[[#Maja Taskovic | Exponential tails for the non-cutoff Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|February 26<br />
| Ashish Kumar Pandey (UIUC)<br />
|[[# | Instabilities in shallow water wave models ]]<br />
| Kim & Lee<br />
|- <br />
|March 5<br />
| Khai Nguyen (NCSU)<br />
|[[#Khai Nguyen | Burgers Equation with Some Nonlocal Sources ]]<br />
| Tran<br />
|- <br />
|March 12<br />
| Hongwei Gao (UCLA)<br />
|[[#Hongwei Gao | Stochastic homogenization of certain nonconvex Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
|March 19<br />
| Huy Nguyen (Princeton)<br />
|[[#Huy Nguyen | Compressible fluids and active potentials ]]<br />
| Lee<br />
|-<br />
|March 26<br />
| <br />
|[[# | Spring recess (Mar 24-Apr 1, 2018) ]]<br />
| <br />
|-<br />
|April 2<br />
| In-Jee Jeong (Princeton)<br />
|[[#In-Jee Jeong | Singularity formation for the 3D axisymmetric Euler equations ]]<br />
| Kim<br />
|- <br />
|April 9<br />
| Jeff Calder (Minnesota)<br />
|[[#Jeff Calder | Nonlinear PDE continuum limits in data science and machine learning ]]<br />
| Tran<br />
|- <br />
|April 21-22 (Saturday-Sunday)<br />
| [https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]<br />
|[[#Midwest PDE seminar | ]]<br />
| Angenent, Feldman, Kim, Tran.<br />
|- <br />
|April 25 (Wednesday)<br />
| Hitoshi Ishii (Wasow lecture)<br />
|[[#Hitoshi Ishii | Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory]]<br />
| Tran.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Dan Knopf===<br />
<br />
Title: Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons<br />
<br />
Abstract: We describe Riemannian (non-K&auml;hler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking K&auml;hler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-K&auml;hler solutions of Ricci flow that become asymptotically K&auml;hler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of K&auml;hler metrics under Ricci flow.<br />
<br />
===Andreas Seeger===<br />
<br />
Title: Singular integrals and a problem on mixing flows<br />
<br />
Abstract: The talk will be about results related to Bressan's mixing problem. We present an inequality for the change of a Bianchini semi-norm of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which one proves bounds on Hardy spaces. This is joint work with Mahir Hadžić, Charles Smart and Brian Street.<br />
<br />
===Sam Krupa===<br />
<br />
Title: Proving Uniqueness of Solutions for Burgers Equation Entropic for a Single Entropy, with Eye Towards Systems Case<br />
<br />
Abstract: For hyperbolic systems of conservation laws, uniqueness of solutions is still largely open. We aim to expand the theory of uniqueness for systems of conservation laws. One difficulty is that many systems have only one entropy. This contrasts with scalar conservation laws, where many entropies exist. It took until 1994 to show that one entropy is enough to ensure uniqueness of solutions for the scalar conservation laws (Panov). This single entropy result was proven again by De Lellis, Otto and Westdickenberg in 2004. These two proofs both rely on the special connection between Hamilton--Jacobi equations and scalar conservation laws in one space dimension. However, this special connection does not extend to systems. In our new work, we prove the single entropy result for scalar conservation laws without using Hamilton--Jacobi. Our proof lays out new techniques that are promising for showing uniqueness of solutions in the systems case. This is joint work with A. Vasseur.<br />
<br />
<br />
===Maja Taskovic===<br />
<br />
Title: Exponential tails for the non-cutoff Boltzmann equation<br />
<br />
Abstract: The Boltzmann equation models the motion of a rarefied gas, in which particles interact through binary collisions, by describing the evolution of the particle density function. The effect of collisions on the density function is modeled by a bilinear integral operator (collision operator) which in many cases has a non-integrable angular kernel. For a long time the equation was simplified by assuming that this kernel is integrable (the so called Grad's cutoff) with a belief that such an assumption does not affect the equation significantly. However, in the last 20 years it has been observed that a non-integrable singularity carries regularizing properties which motivates further analysis of the equation in this setting.<br />
<br />
We study behavior in time of tails of solutions to the Boltzmann equation in the non-cutoff regime by examining the generation and propagation of $L^1$ and $L^\infty$ exponentially weighted estimates and the relation between them. For this purpose we introduce Mittag-Leffler moments which can be understood as a generalization of exponential moments. An interesting aspect of this result is that the singularity rate of the angular kernel affects the order of tails that can be shown to propagate in time. This is based on joint works with Alonso, Gamba, Pavlovic and Gamba, Pavlovic.<br />
<br />
<br />
===Ashish Kumar Pandey===<br />
<br />
Title: Instabilities in shallow water wave models<br />
<br />
Abstract: Slow modulations in wave characteristics of a nonlinear, periodic traveling wave in a dispersive medium may develop non-trivial structures which evolve as it propagates. This phenomenon is called modulational instability. In the context of water waves, this phenomenon was observed by Benjamin and Feir and, independently, by Whitham in Stokes' waves. I will discuss a general mechanism to study modulational instability of periodic traveling waves which can be applied to several classes of nonlinear dispersive equations including KdV, BBM, and regularized Boussinesq type equations.<br />
<br />
<br />
===Khai Nguyen===<br />
<br />
Title: Burgers Equation with Some Nonlocal Sources<br />
<br />
Abstract: Consider the Burgers equation with some nonlocal sources, which were derived from models of nonlinear wave with constant frequency. This talk will present some recent results on the global existence of entropy weak solutions, priori estimates, and a uniqueness result for both Burgers-Poisson and Burgers-Hilbert equations. Some open questions will be discussed.<br />
<br />
===Hongwei Gao=== <br />
<br />
Title: Stochastic homogenization of certain nonconvex Hamilton-Jacobi equations<br />
<br />
Abstract: In this talk, we discuss the stochastic homogenization of certain nonconvex Hamilton-Jacobi equations. The nonconvex Hamiltonians, which are generally uneven and inseparable, are generated by a sequence of (level-set) convex Hamiltonians and a sequence of (level-set) concave Hamiltonians through the min-max formula. We provide a monotonicity assumption on the contact values between those stably paired Hamiltonians so as to guarantee the stochastic homogenization. If time permits, we will talk about some homogenization results when the monotonicity assumption breaks down.<br />
<br />
===Huy Nguyen===<br />
<br />
Title : Compressible fluids and active potentials<br />
<br />
Abstract: We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion coefficients do not vanish, and give local and global existence results. The models include the barotropic compressible Navier-Stokes equations, shallow water systems and the lubrication approximation of slender jets. In all these models the momentum equation is forced by the gradient of a solution-dependent potential: the active potential. The method of proof uses the Bresch-Desjardins entropy and the analysis of the evolution of the active potential.<br />
<br />
===In-Jee Jeong===<br />
<br />
Title: Singularity formation for the 3D axisymmetric Euler equations<br />
<br />
Abstract: We consider the 3D axisymmetric Euler equations on exterior domains $\{ (x,y,z) : (1 + \epsilon|z|)^2 \le x^2 + y^2 \} $ for any $\epsilon > 0$ so that we can get arbitrarily close to the exterior of a cylinder. We construct a strong local well-posedness class, and show that within this class there exist compactly supported initial data which blows up in finite time. The local well-posedness class consists of velocities which are uniformly Lipschitz in space and have finite energy. Our results were inspired by recent works of Hou-Luo, Kiselev-Sverak, and many others, and the proof builds up on our previous works on 2D Euler and Boussinesq systems. This is joint work with Tarek Elgindi.<br />
<br />
===Jeff Calder===<br />
<br />
Title: Nonlinear PDE continuum limits in data science and machine learning<br />
<br />
Abstract: We will present some recent results on PDE continuum limits for (random) discrete problems in data science and machine learning. All of the problems satisfy a type of discrete comparison/maximum principle and so the continuum PDEs are properly interpreted in the viscosity sense. We will present results for nondominated sorting, convex hull peeling, and graph-based semi-supervised learning. Nondominated sorting is an algorithm for arranging points in Euclidean space into layers by repeatedly peeling away coordinatewise minimal points, and the continuum PDE turns out to be a Hamilton-Jacobi equation. Convex hull peeling is used to order data by repeatedly peeling the vertices of the convex hull, and the continuum limit is motion by a power of Gauss curvature. Finally, a recently proposed class of graph-based learning problems have PDE continuum limits corresponding to weighted p-Laplace equations. In each case the continuum PDEs provide insights into the data science/engineering problems, and suggest avenues for fast approximate algorithms based on the PDE interpretations.<br />
<br />
===Hitoshi Ishii===<br />
<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15428Colloquia/Fall182018-04-17T19:29:39Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13 (911 Van Vleck)<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#April 16, Christine Berkesch Zamaere (University of Minnesota)| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday, Room: 911)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Tsuda University) Wasow lecture<br />
|[[#April 25, Hitoshi Ishii (Tsuda University)| Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm, Room: B102 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm, Room: B325 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
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|date<br />
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|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
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|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|-<br />
|date<br />
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|[[# TBA| TBA ]]<br />
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|-<br />
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|[[# TBA| TBA ]]<br />
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|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16, Christine Berkesch Zamaere (University of Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
<br />
===April 25, Hitoshi Ishii (Tsuda University)===<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Blank|Fall 2018]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15416Colloquia/Fall182018-04-15T20:57:28Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13 (911 Van Vleck)<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#April 16, Christine Berkesch Zamaere (University of Minnesota)| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Tsuda University) Wasow lecture<br />
|[[#April 25, Hitoshi Ishii (Tsuda University)| Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm, Room: B102 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm, Room: B325 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16, Christine Berkesch Zamaere (University of Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
<br />
===April 25, Hitoshi Ishii (Tsuda University)===<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Blank|Fall 2018]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldmanhttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15336Colloquia/Fall182018-04-04T21:31:38Z<p>Feldman: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
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|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[# TBA| TBA ]]<br />
| Erman, Sam<br />
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| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
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| Tran<br />
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| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<br />
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== Spring Abstracts ==<br />
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===January 29 Li Chao (Columbia)===<br />
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Title: Elliptic curves and Goldfeld's conjecture<br />
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Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
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=== February 2 Thomas Fai (Harvard) ===<br />
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Title: The Lubricated Immersed Boundary Method<br />
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Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
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===February 5 Alex Lubotzky (Hebrew University)===<br />
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Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
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Abstract: <br />
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Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
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In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
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This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
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===February 6 Alex Lubotzky (Hebrew University)===<br />
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Title: Groups' approximation, stability and high dimensional expanders<br />
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Abstract: <br />
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Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
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The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
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All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
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===February 9 Wes Pegden (CMU)===<br />
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Title: The fractal nature of the Abelian Sandpile <br />
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Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
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Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
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===March 2 Aaron Bertram (Utah)===<br />
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Title: Stability in Algebraic Geometry<br />
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Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
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===March 16 Anne Gelb (Dartmouth)===<br />
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Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
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Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
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===April 5 John Baez (UC Riverside)===<br />
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Title: Monoidal categories of networks<br />
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Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
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===April 6 Edray Goins (Purdue)===<br />
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Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
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Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
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This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
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This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
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== Past Colloquia ==<br />
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[[Colloquia/Blank|Blank Colloquia]]<br />
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[[Colloquia/Fall2017|Fall 2017]]<br />
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[[Colloquia/Spring2017|Spring 2017]]<br />
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[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
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[[Colloquia/Spring2016|Spring 2016]]<br />
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[[Colloquia/Fall2015|Fall 2015]]<br />
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[[Colloquia/Spring2014|Spring 2015]]<br />
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[[Colloquia/Fall2014|Fall 2014]]<br />
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[[Colloquia/Spring2014|Spring 2014]]<br />
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[[Colloquia/Fall2013|Fall 2013]]<br />
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[[Colloquia 2012-2013|Spring 2013]]<br />
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[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Feldman