Difference between revisions of "PDE Geometric Analysis seminar"

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(Jeffery Streets)
(PDE GA Seminar Schedule Fall 2019-Spring 2020)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2017 | Tentative schedule for Fall 2017]]===
+
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===
 +
 
 +
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==
  
= PDE GA Seminar Schedule Spring 2017 =
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
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!align="left" | title
 
!align="left" | title
 
!style="width:20%" align="left" | host(s)
 
!style="width:20%" align="left" | host(s)
|-
+
|-
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck
+
|Sep 9
| Sigurd Angenent (UW)
+
| Scott Smith (UW Madison)
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]
+
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]
| Kim & Tran
+
| Kim and Tran
|-  
+
|-
 
+
|Sep 14-15
|-
+
|  
|January 30
+
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html  ]]
| Serguei Denissov (UW)
+
|
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]
+
|-
| Kim & Tran
+
|Sep 23
|-
+
| Son Tu (UW Madison)
 
+
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]
 
+
| Kim and Tran
|-
+
|-
|February 6 - Wasow lecture
+
|Sep 28-29, VV901
| Benoit Perthame (University of Paris VI)
+
| https://www.ki-net.umd.edu/content/conf?event_id=993
|[[#| ]]
+
|   | Recent progress in analytical aspects of kinetic equations and related fluid models 
| Jin
+
|
|-  
+
|-
 
+
|Oct 7
 
+
| Jin Woo Jang (Postech)
|-
+
|[[#Speaker | TBA ]]
|February 13
+
| Kim
| Bing Wang (UW)
+
|-
|[[#Bing Wang | The extension problem of the mean curvature flow]]
+
|Oct 14
| Kim & Tran
+
| Stefania Patrizi (UT Austin)
|-  
+
|[[#Stefania Patrizi | TBA ]]
 
 
|-
 
|February 20
 
| Eric Baer (UW)
 
|[[#Eric Baer | Isoperimetric sets inside almost-convex cones]]
 
| Kim & Tran
 
|-  
 
 
 
|-
 
|February 27
 
| Ben Seeger (University of Chicago)
 
|[[#Ben Seeger | Homogenization of pathwise Hamilton-Jacobi equations ]]
 
 
| Tran
 
| Tran
|-  
+
|-
 
+
|Oct 21
|-
+
| Claude Bardos (Université Paris Denis Diderot, France)
|March 7 - Mathematics Department Distinguished Lecture
+
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]
| Roger Temam (Indiana University)
+
| Li
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]
+
|-
| Smith  
+
|Oct 28
|-
+
| Albert Ai (UW Madison)
 
+
|[[#Albert Ai | TBA ]]
 
+
| Ifrim
|-
+
|-  
|March 8 - Analysis/Applied math/PDE seminar
+
|Nov 4
| Roger Temam (Indiana University)
+
| Yunbai Cao (UW Madison)
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]
+
|[[#Yunbai Cao | TBA ]]
| Smith
+
| Kim and Tran
|-
+
|-
 
+
|Nov 11
|-
+
| Speaker (Institute)
|March 13
+
|[[#Speaker | TBA ]]
| Sona Akopian (UT-Austin)
+
| Host
|[[#Sona Akopian | Global $L^p$ well posed-ness of the Boltzmann equation with an angle-potential concentrated collision kernel.]]
+
|-
| Kim
+
|Nov 18
 
+
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 
|-
 
|-
|March 27 - Analysis/PDE seminar
+
|Nov 25
| Sylvia Serfaty (Courant)
+
| Mathew Langford (UT Knoxville)
|[[#Sylvia Serfaty | Mean-Field Limits for Ginzburg-Landau vortices ]]
+
|[[#Speaker | TBA ]]
 +
| Angenent
 +
|-
 +
|-
 +
|Feb 17
 +
| Yannick Sire (JHU)
 +
|[[#Yannick Sire (JHU) | TBA ]]
 
| Tran
 
| Tran
 
+
|- 
|-
+
|Feb 24
|March 29 - Wasow lecture
+
| Speaker (Institute)
| Sylvia Serfaty (Courant)
+
|[[#Speaker | TBA ]]
|[[#Sylvia Serfaty | Microscopic description of Coulomb-type systems ]]
+
| Host
|  
+
|-
 
+
|March 2
 
+
| Theodora Bourni (UT Knoxville)
|-
+
|[[#Speaker | TBA ]]
|March 30 <br>Special day (Thursday) and location:<br> B139 Van Vleck
+
| Angenent
| Gui-Qiang Chen (Oxford)
+
|-
|[[#Gui-Qiang Chen | Supersonic Flow onto Solid Wedges,
+
|March 9
Multidimensional Shock Waves and Free Boundary Problems ]]
+
| Speaker (Institute)
| Feldman
+
|[[#Speaker | TBA ]]
 
+
| Host
 
+
|- 
 
+
|March 16
|-
+
| No seminar (spring break)
|April 3
+
|[[#Speaker | TBA ]]
| Zhenfu Wang (Maryland)
+
| Host
|[[#Zhenfu Wang | Mean field limit for stochastic particle systems with singular forces]]
+
|-
 +
|March 23
 +
| Jared Speck (Vanderbilt)
 +
|[[#Jared Speck | TBA ]]
 +
| SCHRECKER
 +
|-  
 +
|March 30
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|-   
 +
|April 6
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|April 13
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|-
 +
|April 20
 +
| Hyunju Kwon (IAS)
 +
|[[#Hyunju Kwon | TBA ]]
 
| Kim
 
| Kim
 
+
|-
|-
+
|April 27
|April 10
+
| Speaker (Institute)
| Andrei Tarfulea (Chicago)
+
|[[#Speaker | TBA ]]
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]
+
| Host
| Baer
 
 
 
|-
 
|April 17
 
| Siao-Hao Guo (Rutgers)
 
|[[# Siao-Hao Guo | Analysis of Velázquez's solution to the mean curvature flow with a type II singularity]]
 
| Lu Wang
 
 
 
 
 
|-
 
|April 24
 
| Jianfeng Lu
 
|[[#Jianfeng Lu | TBA]]
 
| Li
 
 
 
|-
 
|April 25- joint Analysis/PDE seminar
 
| Chris Henderson (Chicago)
 
|[[#Chris Henderson | TBA]]
 
| Lin
 
 
 
|-
 
|May 1st
 
| Jeffrey Streets (UC-Irvine)
 
|[[#Jeffrey Streets | Generalized Kahler Ricci flow and a generalized Calabi conjecture]]
 
| Bing Wang
 
 
|}
 
|}
  
=Abstracts=
+
== Abstracts ==
 
 
===Sigurd Angenent===
 
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so.  Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo;  In doing so one finds that there is interesting dynamics associated to ancient solutions.  I will discuss what is currently known about these solutions.  Some of the talk is based on joint work with Sesum and Daskalopoulos.
 
 
 
===Serguei Denissov===
 
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.
 
 
 
 
 
===Bing Wang===
 
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.
 
 
 
===Eric Baer===
 
We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones.  Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere.  The work we describe is joint with A. Figalli.
 
 
 
===Ben Seeger===
 
I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.
 
 
 
===Sona Akopian===
 
Global $L^p$ well posed-ness of the Boltzmann equation with an angle-potential concentrated collision kernel.
 
 
 
We solve the Cauchy problem associated to an epsilon-parameter family of homogeneous Boltzmann equations for very soft and Coulomb potentials. Proposed in 2013 by Bobylev and Potapenko, the collision kernel that we use is a Dirac mass concentrated at very small angles and relative speeds. The main advantage of such a kernel is that it does not separate its variables (relative speed $u$ and scattering angle $\theta$) and can be viewed as a pseudo-Maxwell molecule collision kernel, which allows for the splitting of the Boltzmann collision operator into its gain and loss terms. Global estimates on the gain term gives us an existence theory for $L^1_k \capL^p$ with any $k\geq 2$ and $p\geq 1.$ Furthermore the bounds we obtain are independent of the epsilon parameter, which allows for analysis of the solutions in the grazing collisions limit, i.e., when epsilon approaches zero and the Boltzmann equation becomes the Landau equation.
 
 
 
===Sylvia Serfaty===
 
Mean-Field Limits for Ginzburg-Landau vortices
 
 
 
Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.
 
 
 
 
 
===Gui-Qiang Chen===
 
Supersonic Flow onto Solid Wedges, Multidimensional Shock Waves and Free Boundary Problems
 
 
 
When an upstream steady uniform supersonic flow, governed by the Euler equations,
 
impinges onto a symmetric straight-sided wedge, there are two possible steady oblique shock
 
configurations if the wedge angle is less than the detachment angle -- the steady weak shock
 
with supersonic or subsonic downstream flow (determined by the wedge angle that is less or larger
 
than the sonic angle) and the steady strong shock with subsonic downstream flow, both of which
 
satisfy the entropy conditions.
 
The fundamental issue -- whether one or both of the steady weak and strong shocks are physically
 
admissible solutions -- has been vigorously debated over the past eight decades.
 
In this talk, we discuss some of the most recent developments on the stability analysis
 
of the steady shock solutions in both the steady and dynamic regimes.
 
The corresponding stability problems can be formulated as free boundary problems
 
for nonlinear partial differential equations of mixed elliptic-hyperbolic type, whose
 
solutions are fundamental for multidimensional hyperbolic conservation laws.
 
Some further developments, open problems, and mathematical challenges in this direction
 
are also addressed.
 
 
 
===Zhenfu Wang===
 
  
Title: Mean field limit for stochastic particle systems with singular forces
+
===Scott Smith===
  
Abstract: We consider large systems of particles interacting through rough interaction kernels. We are able to control the relative entropy between the N-particles distribution
+
Title: Recent progress on singular, quasi-linear stochastic PDE
and the expected limit which solves the corresponding McKean-Vlasov PDE. This implies the Mean Field limit to the McKean-Vlasov system together with Propagation of Chaos
 
through the strong convergence of all the marginals. The method works at the level of the Liouville equation and relies on precise combinatorics results.
 
  
===Andrei Tarfulea===
+
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.
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and
 
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.
 
  
===Siao-hao Guo===
 
Analysis of Velázquez's solution to the mean curvature flow with a type II singularity
 
  
Velázquez discovered a solution to the mean curvature flow which develops a type II singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution, the rescaled flow converges in the C^0 sense to a minimal hypersurface which is tangent to Simons' cone at infinity. In this talk, we will present that the rescaled flow actually converges locally smoothly to the minimal hypersurface, which appears to be the singularity model of the type II singularity. In addition, we will show that the mean curvature of the solution blows up near the origin at a rate which is smaller than that of the second fundamental form. This is a joint work with N. Sesum.
+
===Son Tu===
  
===Jeffrey Streets===
+
Title: State-Constraint static Hamilton-Jacobi equations in nested domains
  
Generalized Kahler geometry is a natural extension of Kahler geometry with roots in mathematical physics, and is a particularly rich instance of Hitchin's program of `generalized geometries.'  In this talk I will discuss an extension of Kahler-Ricci flow to this setting.  I will formulate a natural Calabi-Yau type conjecture based on Hitchin/Gualtieri's definition of generalized Calabi-Yau equations, then introduce the flow as a tool for resolving thisThe main result is a global existence and convergence result for the flow which yields a partial resolution of this conjecture, and which classifies generalized Kahler structures on hyperKahler backgrounds.
+
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).

Latest revision as of 11:37, 19 September 2019

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Previous PDE/GA seminars

Tentative schedule for Fall 2020-Spring 2021

PDE GA Seminar Schedule Fall 2019-Spring 2020

date speaker title host(s)
Sep 9 Scott Smith (UW Madison) Recent progress on singular, quasi-linear stochastic PDE Kim and Tran
Sep 14-15 AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html
Sep 23 Son Tu (UW Madison) State-Constraint static Hamilton-Jacobi equations in nested domains Kim and Tran
Sep 28-29, VV901 https://www.ki-net.umd.edu/content/conf?event_id=993 Recent progress in analytical aspects of kinetic equations and related fluid models
Oct 7 Jin Woo Jang (Postech) TBA Kim
Oct 14 Stefania Patrizi (UT Austin) TBA Tran
Oct 21 Claude Bardos (Université Paris Denis Diderot, France) From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture Li
Oct 28 Albert Ai (UW Madison) TBA Ifrim
Nov 4 Yunbai Cao (UW Madison) TBA Kim and Tran
Nov 11 Speaker (Institute) TBA Host
Nov 18 Speaker (Institute) TBA Host
Nov 25 Mathew Langford (UT Knoxville) TBA Angenent
Feb 17 Yannick Sire (JHU) TBA Tran
Feb 24 Speaker (Institute) TBA Host
March 2 Theodora Bourni (UT Knoxville) TBA Angenent
March 9 Speaker (Institute) TBA Host
March 16 No seminar (spring break) TBA Host
March 23 Jared Speck (Vanderbilt) TBA SCHRECKER
March 30 Speaker (Institute) TBA Host
April 6 Speaker (Institute) TBA Host
April 13 Speaker (Institute) TBA Host
April 20 Hyunju Kwon (IAS) TBA Kim
April 27 Speaker (Institute) TBA Host

Abstracts

Scott Smith

Title: Recent progress on singular, quasi-linear stochastic PDE

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.


Son Tu

Title: State-Constraint static Hamilton-Jacobi equations in nested domains

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).