Difference between revisions of "PDE Geometric Analysis seminar"

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(Seminar Schedule Fall 2014)
(PDE GA Seminar Schedule Fall 2019-Spring 2020)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Spring 2015 | Tentative schedule for Spring 2015]]===
+
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===
 +
 
 +
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==
 +
 
  
= Seminar Schedule Fall 2014 =
 
 
{| cellpadding="8"
 
{| cellpadding="8"
!align="left" | date   
+
!style="width:20%" align="left" | date   
 
!align="left" | speaker
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | title
!align="left" | host(s)
+
!style="width:20%" align="left" | host(s)
|-
+
|-
|September 15
+
|Sep 9
|Greg Kuperberg (UC-Davis)
+
| Scott Smith (UW Madison)
|[[#Greg Kuperberg (UC-Davis) | ''Cartan-Hadamard and the Little Prince'' ]]
+
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]
|Viaclovsky
+
| Kim and Tran
|-
+
|-
|-
+
|Sep 14-15
|September 22 (joint with Analysis Seminar)
+
|  
|Steve Hofmann (U. of Missouri)
+
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html  ]]
|[[#Steven Hofmann (U. of Missouri) |    ''Quantitative Rectifiability and Elliptic Equations'']]
+
|
|Seeger
+
|-
|-
+
|Sep 23
|-
+
| Son Tu (UW Madison)
|Oct 6th,
+
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]
|Xiangwen Zhang (Columbia University)
+
| Kim and Tran
|[[#Xiangwen Zhang (Columbia University) |Alexandrov's Uniqueness Theorem for Convex Surfaces ]]
+
|-
|B.Wang
+
|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 
|October 13
+
|Xuwen Chen (Brown University)[http://www.math.brown.edu/~chenxuwen/]
+
|- 
|[[#Xuwen Chen (Brown University) |
+
|Oct 7
TBA]]
+
| Jin Woo Jang (Postech)
|C.Kim
+
|[[#Speaker | TBA ]]
|-
+
| Kim
|-
+
|-
|October 20
+
|Oct 14
|Kyudong Choi (UW-Madison)
+
| Stefania Patrizi (UT Austin)
|[[#Kyudong Choi (UW-Madison) |
+
|[[#Stefania Patrizi | TBA ]]
Finite time blow up for 1D models for the 3D Axisymmetric Euler Equations the 2D Boussinesq system]]
+
| Tran
|C.Kim
+
|-
|-
+
|Oct 21
|-
+
| Claude Bardos (Université Paris Denis Diderot, France)
|October 27
+
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]
|Chanwoo Kim (UW-Madison)
+
| Li
|[[#Chanwoo Kim (UW-Madison) |
+
|-
BV-Regularity of the Boltzmann Equation in Non-Convex Domains]]
+
|Oct 28
|Local
+
| Albert Ai (UW Madison)
|-
+
|[[#Albert Ai | TBA ]]
|-
+
| Ifrim
|November 10
+
|-
|Philip Isett (MIT)
+
|Nov 4
|[[#Philip Isett (MIT) | TBA ]]
+
| Yunbai Cao (UW Madison)
|C.Kim
+
|[[#Yunbai Cao | TBA ]]
|-
+
| Kim and Tran
|-
+
|-
|November 17
+
|Nov 11
|Lei Wu
+
| Speaker (Institute)
|[[#Lei Wu | Geometric Correction for Diffusive Expansion in Neutron Transport Equation  ]]
+
|[[#Speaker | TBA ]]
|C.Kim
+
| Host
|-
+
|-
|-
+
|Nov 18
|November 24
+
| Speaker (Institute)
|Hongnian Huang (Univeristy of New Mexico)
+
|[[#Speaker | TBA ]]
|[[#Hongnian Huang (UNM) | TBA ]]
+
| Host
|B.Wang
 
 
|-
 
|-
 +
|Nov 25
 +
| Mathew Langford (UT Knoxville)
 +
|[[#Speaker | TBA ]]
 +
| Angenent
 +
|- 
 +
|- 
 +
|Feb 17
 +
| Yannick Sire (JHU)
 +
|[[#Yannick Sire (JHU) | TBA ]]
 +
| Tran
 +
|- 
 +
|Feb 24
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|March 2
 +
| Theodora Bourni (UT Knoxville)
 +
|[[#Speaker | TBA ]]
 +
| Angenent
 +
|- 
 +
|March 9
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|March 16
 +
| No seminar (spring break)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|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
 +
|- 
 +
|April 27
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 
|}
 
|}
  
== Fall Abstracts ==
+
== Abstracts ==
 
 
===Greg Kuperberg===
 
''Cartan-Hadamard and the Little Prince.''
 
 
 
===Steve Hofmann===
 
''Quantitative Rectifiability and Elliptic Equations''
 
  
A classical theorem of F. and M. Riesz states that for a simply connected domain in the complex plane with a rectifiable boundary, harmonic measure and arc length measure on the boundary are mutually absolutely continuous. On the other hand, an example of C. Bishop and P. Jones shows that the latter conclusion may fail, in the absence of some sort of connectivity hypothesis. In this talk, we discuss recent developments in an ongoing program to find scale-invariant, higher dimensional versions of the F. and M. Riesz Theorem, as well as converses. In particular, we discuss substitute results that continue to hold in the absence of any connectivity hypothesis.
+
===Scott Smith===
  
===Xiangwen Zhang===
+
Title: Recent progress on singular, quasi-linear stochastic PDE
''Alexandrov's Uniqueness Theorem for Convex Surfaces''
 
  
A classical uniqueness theorem of Alexandrov says that: a closed strictly convex twice differentiable surface in R3 is uniquely determined to within a parallel translation when one gives a proper function of the principle curvatures. We will talk about a PDE proof for this thorem, by using the maximal principle and weak uniqueness continuation theorem of Bers-Nirenberg. Moreover, a stability result related to the uniqueness problem will be mentioned. This is a joint work with P. Guan and Z. Wang.
+
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.
If time permits, we will also briefly introduce the idea of our recent work on Alexandrov’s theorems for codimension two submanifolds in spacetimes.
 
  
===Kyudong Choi===
 
''Finite time blow up for 1D models for the 3D Axisymmetric Euler Equations the
 
2D Boussinesq system''
 
  
In connection with the recent proposal for possible singularity formation at the boundary for solutions of the 3d axi-symmetric incompressible Euler's equations / the 2D Boussinesq system (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data. This is joint work with T. Hou, A. Kiselev, G. Luo, V. Sverak, and Y. Yao.
+
===Son Tu===
  
===Lei Wu===
+
Title: State-Constraint static Hamilton-Jacobi equations in nested domains
''Geometric Correction for Diffusive Expansion in Neutron Transport Equation''
 
  
We revisit the diffusive limit of a steady neutron transport equation in a 2-D unit disk with one-speed velocity. The traditional method is Hilbert expansions and boundary layer analysis. We will carefully study the classical theory of the construction of boundary layers, and discuss the necessity and specific method to add the geometric correction.
+
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).