https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Ckim&feedformat=atomUW-Math Wiki - User contributions [en]2020-07-07T10:24:38ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19289PDE Geometric Analysis seminar2020-03-23T14:08:33Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23 (CANCELLED)<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30 (CANCELLED)<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (CANCELLED, will be rescheduled)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | (CANCELLED) Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13 (CANCELLED)<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 (CANCELLED)<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | (CANCELLED) On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27 <br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | ]]<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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19288PDE Geometric Analysis seminar2020-03-23T14:08:11Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23 (CANCELLED)<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30 (CANCELLED)<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (CANCELLED)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | (CANCELLED) Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13 (CANCELLED)<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 (CANCELLED)<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | (CANCELLED) On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27 <br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | ]]<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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19287PDE Geometric Analysis seminar2020-03-23T13:28:22Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23 (CANCELLED)<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30 (CANCELLED)<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (CANCELLED)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | (CANCELLED) Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13 (CANCELLED)<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 (CANCELLED)<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | (CANCELLED) On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27 (CANCELLED)<br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | CANCELLED ]]<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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19286PDE Geometric Analysis seminar2020-03-23T13:27:41Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (CANCELLED)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | (CANCELLED) Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 (CANCELLED)<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | (CANCELLED) On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27 (CANCELLED)<br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19284PDE Geometric Analysis seminar2020-03-20T18:01:00Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (CANCELLE, will be rescheduled later)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | (CANCELLED) Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 (CANCELLED)<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | (CANCELLED) On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27<br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19283PDE Geometric Analysis seminar2020-03-20T17:58:45Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (will be rescheduled)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 (CANCELLED)<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | (CANCELLED) On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27<br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19282PDE Geometric Analysis seminar2020-03-20T17:58:20Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (will be rescheduled)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<br />
| Kim<br />
|- <br />
|April 20 CANCELLED<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27<br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19257PDE Geometric Analysis seminar2020-03-12T18:25:06Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (will be rescheduled)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19256PDE Geometric Analysis seminar2020-03-12T18:24:40Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6 (rescheduling)<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19238PDE Geometric Analysis seminar2020-03-11T21:04:54Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | CANCELLED ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | CANCELLED ]]<br />
| Kim and Tran<br />
|- <br />
|April 6<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | CANCELLED ]]<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19237PDE Geometric Analysis seminar2020-03-11T20:23:04Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | cancelled ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|April 6<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | Cancelled ]]<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19236PDE Geometric Analysis seminar2020-03-11T20:07:46Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | cancelled ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|April 6<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19235PDE Geometric Analysis seminar2020-03-11T20:06:36Z<p>Ckim: /* 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 | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 | (cancelled) ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|April 6<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=19187PDE Geometric Analysis seminar2020-03-03T20:52:57Z<p>Ckim: </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 | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| Traveling wave solutions to the free boundary Navier-Stokes equations ]]<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 />
| Kim and Tran<br />
|- <br />
|April 6<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<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 />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | 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 />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Ian Tice===<br />
Title: Traveling wave solutions to the free boundary Navier-Stokes equations<br />
<br />
Abstract: Consider a layer of viscous incompressible fluid bounded below<br />
by a flat rigid boundary and above by a moving boundary. The fluid is<br />
subject to gravity, surface tension, and an external stress that is<br />
stationary when viewed in coordinate system moving at a constant<br />
velocity parallel to the lower boundary. The latter can model, for<br />
instance, a tube blowing air on the fluid while translating across the<br />
surface. In this talk we will detail the construction of traveling wave<br />
solutions to this problem, which are themselves stationary in the same<br />
translating coordinate system. While such traveling wave solutions to<br />
the Euler equations are well-known, to the best of our knowledge this is<br />
the first construction of such solutions with viscosity. This is joint<br />
work with Giovanni Leoni.<br />
<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=19186Putnam Club2020-03-03T19:27:01Z<p>Ckim: </p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2020.<br />
<br />
<br />
<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] Botong<br />
* March 4 and 11: [[Media: Inequalities.pdf | Inequalities]] ( Note comming up!) Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=19185Putnam Club2020-03-03T19:26:21Z<p>Ckim: /* Spring 2020 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2020.<br />
<br />
<br />
<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] Botong<br />
* March 4 and 11: [[Media: | Inequalities]] Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Fall_2020-Spring_2021&diff=19075Fall 2020-Spring 20212020-02-20T17:18:47Z<p>Ckim: /* PDE GA Seminar Schedule Fall 2020-Spring 2021 */</p>
<hr />
<div>== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<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 />
|Oct 5 <br />
| Daniel Spirn (Minneapolis)<br />
|[[# | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 26 <br />
| Tarek Elgindi (UCSD)<br />
|[[# | TBA ]]<br />
| Kim<br />
|}</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18892PDE Geometric Analysis seminar2020-02-05T13:39:51Z<p>Ckim: </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 />
| 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.<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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18891PDE Geometric Analysis seminar2020-02-05T13:39:40Z<p>Ckim: /* =Joonhyun La */</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 />
| 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.<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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18890PDE Geometric Analysis seminar2020-02-05T13:39:30Z<p>Ckim: </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 />
| 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.<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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18536PDE Geometric Analysis seminar2019-12-09T15:12:03Z<p>Ckim: /* 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 Université)<br />
|[[#Speaker | TBA ]]<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18527PDE Geometric Analysis seminar2019-12-05T21:52:27Z<p>Ckim: /* 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 Université)<br />
|[[#Speaker | TBA ]]<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 />
| 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.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18525PDE Geometric Analysis seminar2019-12-05T19:24:53Z<p>Ckim: </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 Université)<br />
|[[#Speaker | TBA ]]<br />
| Feldman<br />
|- <br />
|Feb. 10<br />
| TBA (TBA)<br />
|[[#Speaker | 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 />
| 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.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18524PDE Geometric Analysis seminar2019-12-05T19:22:05Z<p>Ckim: /* 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 Université)<br />
|[[#Speaker | TBA ]]<br />
| Feldman<br />
|- <br />
|Feb. 10<br />
| TBA (TBA)<br />
|[[#Speaker | TBA ]]<br />
| Chanwoo<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.<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>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Fall_2020-Spring_2021&diff=18405Fall 2020-Spring 20212019-11-12T22:02:44Z<p>Ckim: /* PDE GA Seminar Schedule Fall 2020-Spring 2021 */</p>
<hr />
<div>== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<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 />
|Oct 5 <br />
| Daniel Spirn (Minneapolis)<br />
|[[# | TBA ]]<br />
| Kim<br />
|}</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18340PDE Geometric Analysis seminar2019-11-06T22:04:18Z<p>Ckim: /* 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 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 />
| 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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18323PDE Geometric Analysis seminar2019-11-04T17:17:09Z<p>Ckim: /* 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 | 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 />
| 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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=18239Research at UW-Madison in DifferentialEquations2019-10-24T13:39:24Z<p>Ckim: </p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Previous events==<br />
<br />
The 81st Midwest PDE seminar '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' was held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] (Moscow State University, 1982) Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE.<br />
<br />
<br />
<br />
==Faculty in related areas==<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denisov] (Moscow State University, 1999) Analysis, PDE.<br />
<br />
[http://www.math.wisc.edu/~qinli/ Qin Li] (UW Madison, 2013) Numerical analysis and scientific computing.<br />
<br />
[http://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie] (Courant Institute, 2008) Fluid dynamics, complex fluids, soft matter, computation.<br />
<br />
[http://www.math.wisc.edu/~stechmann/ Sam Stechmann] (Courant Institute, 2008) Applied math, computational math, fluid dynamics, atmospheric science, climate.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin, 1998) Mixing in fluids, optimization of mixing.<br />
<br />
==Former Postdocs in PDE==<br />
<br />
[http://people.math.gatech.edu/~yyao9/ Yao Yao] (VV assist prof 2012-2015) Current position: Assistant Professor, Georgia Institute of Technology (2015-)<br />
<br />
[https://sites.google.com/view/jessicalin-math/home Jessica Lin] (VV assist prof 2014-2017) Current position: Assistant Professor, McGill University (2017-)<br />
<br />
[https://sites.google.com/site/donghyunlee295/ Donghyun Lee] (VV assist prof 2015-2018) Current position: Assistant Professor, Postech (2018-) <br />
<br />
[https://cam.uchicago.edu/people/profile/eric-baer/ Eric Baer] (VV assist prof 2015-2018) Current position: Senior Lecturer, University of Chicago (2019-)<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynamical Systems, Nonlinear Analysis.<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations.<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=ODE.pdf&diff=18201ODE.pdf2019-10-16T19:07:28Z<p>Ckim: </p>
<hr />
<div>https://chanwookim.files.wordpress.com/2019/10/20191016135940651.pdf</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=ODE.pdf&diff=18200ODE.pdf2019-10-16T19:04:48Z<p>Ckim: Created page with "/Users/ckim/Library/Group Containers/3L68KQB4HG.group.com.readdle.smartemail/databases/messagesData/1/43401/20191016135940651.pdf"</p>
<hr />
<div>/Users/ckim/Library/Group Containers/3L68KQB4HG.group.com.readdle.smartemail/databases/messagesData/1/43401/20191016135940651.pdf</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=18199Putnam Club2019-10-16T19:04:32Z<p>Ckim: /* Fall 2019 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
The Virginia Tech Regional Mathematics Contest is on Oct 26, 9:00-11:30am. The location is to be announced. [https://docs.google.com/forms/d/e/1FAIpQLSfLFgT77SQxbZYN-vQUktsSsekWWITvLf0oiNOYxjCD55oIkg/viewform?usp=sf_link/ Please click this link to register. ]<br />
<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=18198Putnam Club2019-10-16T19:03:19Z<p>Ckim: /* Fall 2019 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
The Virginia Tech Regional Mathematics Contest is on Oct 26, 9:00-11:30am. The location is to be announced. [https://docs.google.com/forms/d/e/1FAIpQLSfLFgT77SQxbZYN-vQUktsSsekWWITvLf0oiNOYxjCD55oIkg/viewform?usp=sf_link/ Please click this link to register. ]<br />
<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[Putnam.pdf | ODE of the first order]] Chanwoo<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=18197Putnam Club2019-10-16T19:02:19Z<p>Ckim: /* Fall 2019 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
The Virginia Tech Regional Mathematics Contest is on Oct 26, 9:00-11:30am. The location is to be announced. [https://docs.google.com/forms/d/e/1FAIpQLSfLFgT77SQxbZYN-vQUktsSsekWWITvLf0oiNOYxjCD55oIkg/viewform?usp=sf_link/ Please click this link to register. ]<br />
<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ | ODE of the first order]] Chanwoo<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18186PDE Geometric Analysis seminar2019-10-15T18:45:46Z<p>Ckim: /* 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 | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18083PDE Geometric Analysis seminar2019-10-02T06:52:24Z<p>Ckim: /* Abstracts */</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 | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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.</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18082PDE Geometric Analysis seminar2019-10-02T06:51:54Z<p>Ckim: /* 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 | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=18051PDE Geometric Analysis seminar2019-09-30T20:33:19Z<p>Ckim: /* 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 />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17957PDE Geometric Analysis seminar2019-09-19T16:37:53Z<p>Ckim: /* 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 />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17956PDE Geometric Analysis seminar2019-09-19T16:37:30Z<p>Ckim: /* 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 />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17955PDE Geometric Analysis seminar2019-09-19T16:37:17Z<p>Ckim: /* 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 />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17954PDE Geometric Analysis seminar2019-09-19T16:36:59Z<p>Ckim: /* 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 />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17953PDE Geometric Analysis seminar2019-09-19T16:36:34Z<p>Ckim: /* 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 />
| <br />
|[[#https://www.ki-net.umd.edu/content/conf?event_id=993 link| Recent progress in analytical aspects of kinetic equations and related fluid models ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17952PDE Geometric Analysis seminar2019-09-19T16:36:12Z<p>Ckim: /* 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 />
| <br />
|[[#https://www.ki-net.umd.edu/content/conf?event_id=993 | Recent progress in analytical aspects of kinetic equations and related fluid models ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17951PDE Geometric Analysis seminar2019-09-19T16:35:54Z<p>Ckim: /* 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 />
| <br />
|[[#[https://www.ki-net.umd.edu/content/conf?event_id=993] | Recent progress in analytical aspects of kinetic equations and related fluid models ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17950PDE Geometric Analysis seminar2019-09-19T16:35:33Z<p>Ckim: /* 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 />
| <br />
|[[# | [https://www.ki-net.umd.edu/content/conf?event_id=993 Recent progress in analytical aspects of kinetic equations and related fluid models ] ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17949PDE Geometric Analysis seminar2019-09-19T16:35:16Z<p>Ckim: /* 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 />
| <br />
|[[# | [Recent progress in analytical aspects of kinetic equations and related fluid models https://www.ki-net.umd.edu/content/conf?event_id=993] ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17948PDE Geometric Analysis seminar2019-09-19T16:33:24Z<p>Ckim: /* 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 />
| <br />
|[[# | Recent progress in analytical aspects of kinetic equations and related fluid models https://www.ki-net.umd.edu/content/conf?event_id=993 ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17921PDE Geometric Analysis seminar2019-09-18T16:36:35Z<p>Ckim: /* 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 />
| AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html<br />
|[[ # | ]]<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 />
| Recent progress in analytical aspects of kinetic equations and related fluid models https://www.ki-net.umd.edu/content/conf?event_id=993<br />
|[[# | ]]<br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17920PDE Geometric Analysis seminar2019-09-18T16:17:45Z<p>Ckim: /* 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 />
| AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html<br />
|[[ # | ]]<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 />
| Recent progress in analytical aspects of kinetic equations and related fluid models https://www.ki-net.umd.edu/content/conf?event_id=993<br />
|[[# | ]]<br />
| <br />
|- <br />
|Sep 30<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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).</div>Ckimhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=17883PDE Geometric Analysis seminar2019-09-16T00:14:40Z<p>Ckim: /* 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 />
| AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html<br />
|[[ # | ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| Recent progress in analytical aspects of kinetic equations and related fluid models https://www.ki-net.umd.edu/content/conf?event_id=993<br />
|[[# | ]]<br />
| <br />
|- <br />
|Sep 30<br />
| Michael Loss (Georgia tech)<br />
|[[#Michael Loss | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<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 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<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 />
<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.</div>Ckim