Difference between revisions of "PDE Geometric Analysis seminar"

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(Seminar Schedule Fall 2014)
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===[[Spring 2015 | Tentative schedule for Spring 2015]]===
 
===[[Spring 2015 | Tentative schedule for Spring 2015]]===
  
= Seminar Schedule Fall 2014 =
+
= Seminar Schedule Spring 2015 =
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date   
 
!align="left" | date   
!align="left" | speaker                  
+
!align="left" | speaker
 
!align="left" | title
 
!align="left" | title
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 15
+
|January 26
|Greg Kuperberg (UC-Davis)
+
|  
|[[#Greg Kuperberg''Cartan-Hadamard and the Little Prince'' ]]
+
|[[# |  ]]
|Viaclovsky
+
|  
 
|-
 
|-
 +
|February 2
 +
|Jessica Lin (Madison)
 +
|[[#Jessica Lin (Madison)  | TBA ]]
 +
|Kim
 
|-
 
|-
|September 22 (joint with Analysis Seminar)
+
|February 9
|Steve Hofmann (U. of Missouri)
+
|  
|[[#Steve Hofmann| ''Quantitative Rectifiability and Elliptic Equations'']]
+
|[[# | ]]
|Seeger
+
|  
 
|-
 
|-
 +
|February 16
 +
|
 +
|[[#  |  ]]
 +
|
 
|-
 
|-
|Oct 6th,
+
|February 23
|Xiangwen Zhang (Columbia University)
+
|Jennifer Beichman (Madison)
|[[#Xiangwen Zhang |Alexandrov's Uniqueness Theorem for Convex Surfaces ]]
+
|[[#Jennifer Beichman (Madison)  | TBA ]]
|B.Wang
+
| Kim
 
|-
 
|-
 +
|March 2
 +
|Benoit Pausader (Princeton)
 +
|[[#Benoit Pausader (Princeton) | TBA]]
 +
|Kim
 
|-
 
|-
|October 13
+
|March 9
|Xuwen Chen (Brown University)[http://www.math.brown.edu/~chenxuwen/]
+
|  
|[[#Xuwen Chen| The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation from 3D Quantum Many-body Evolution]]
+
|[[# | ]]
|C.Kim
+
|  
 
|-
 
|-
 +
|March 16
 +
|
 +
|[[#  |  ]]
 +
|
 
|-
 
|-
|October 20
+
|March 23
|Kyudong Choi (UW-Madison)
+
|  
|[[#Kyudong Choi| Finite time blow up for 1D models for the 3D Axisymmetric Euler Equations the 2D Boussinesq system]]
+
|[[# | ]]
|C.Kim
+
|  
 
|-
 
|-
 +
|March 30
 +
| Spring recess Mar 28-Apr 5 (S-N)
 +
|[[#  |  ]]
 +
|
 
|-
 
|-
|October 27
+
|April 6
|Chanwoo Kim (UW-Madison)
+
|  
|[[#Chanwoo Kim|
+
|[[# | ]]
BV-Regularity of the Boltzmann Equation in Non-Convex Domains]]
+
|  
|Local
 
 
|-
 
|-
 +
|April 13
 +
|
 +
|[[#  |  ]]
 +
|
 
|-
 
|-
|November 3
+
|April 20
|Myoungjean Bae (POSTECH)
+
|Yuan Lou (Ohio State)
|[[#Myoungjean Bae| Recent progress on study of Euler-Poisson system ]]
+
|[[#Yuan Lou (Ohio State) | TBA]]
|M.Feldman
+
|Zlatos
 
|-
 
|-
 +
|April 27
 +
|
 +
|[[#  |  ]]
 +
|
 
|-
 
|-
|November 10
+
|May 4
|Philip Isett (MIT)
+
|  
|[[#Philip Isett|  Hölder Continuous Euler Flows ]]
+
|[[#  |  ]]
|C.Kim
+
|  
|-
 
|-
 
|November 17
 
|Lei Wu
 
|[[#Lei Wu | Geometric Correction for Diffusive Expansion in Neutron Transport Equation ]]
 
|C.Kim
 
|-
 
|-
 
|December 1
 
|[http://orion.math.iastate.edu/xhnguyen Xuan Hien Nguyen] (Iowa State University)
 
|[[#Xuan Hien NguyenGluing constructions for self-similar surfaces under mean curvature flow ]]
 
|Angenent
 
 
|-
 
|-
 
|}
 
|}
  
== Fall 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.
 
 
===Xiangwen Zhang===
 
''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.
 
If time permits, we will also briefly introduce the idea of our recent work on Alexandrov’s theorems for codimension two submanifolds in spacetimes.
 
 
===Xuwen Chen===
 
''The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation from 3D Quantum Many-body Evolution''
 
 
We consider the focusing 3D quantum many-body dynamic which models a dilute bose gas strongly confined in two spatial directions. We assume that the microscopic pair interaction is focusing and matches the Gross-Pitaevskii scaling condition. We carefully examine the effects of the fine interplay between the strength of the confining potential and the number of particles on the 3D N-body dynamic. We overcome the difficulties generated by the attractive interaction in 3D and establish new focusing energy estimates. We study the corresponding BBGKY hierarchy which contains a diverging coefficient as the strength of the confining potential tends to infinity. We prove that the limiting structure of the density matrices counterbalances this diverging coefficient. We establish the convergence of the BBGKY sequence and hence the propagation of chaos for the focusing quantum many-body system. We derive rigorously the 1D focusing cubic NLS as the mean-field limit of this 3D focusing quantum many-body dynamic and obtain the exact 3D to 1D coupling constant.
 
 
===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.
 
 
===Myoungjean Bae===
 
''Recent progress on study of Euler-Poisson system''
 
 
In this talk, I will present recent progress on the following subjects:
 
(1) Smooth transonic flow of Euler-Poisson system;
 
(2) Transonic shock of Euler-Poisson system.
 
This talk is based on collaboration with Ben Duan, Chujing Xie and Jingjing Xiao
 
 
===Philip Isett===
 
"Hölder Continuous Euler Flows"
 
 
Motivated by the theory of hydrodynamic turbulence, L. Onsager conjectured
 
in 1949 that solutions to the incompressible Euler equations with Holder
 
regularity less than 1/3 may fail to conserve energy.  C. De Lellis and L.
 
Székelyhidi, Jr. have pioneered an approach to constructing such irregular
 
flows based on an iteration scheme known as convex integration.  This
 
approach involves correcting “approximate solutions" by adding rapid
 
oscillations which are designed to reduce the error term in solving the
 
equation.  In this talk, I will discuss an improved convex integration
 
framework, which yields solutions with Holder regularity 1/5-, as well as
 
other related results.
 
 
===Lei Wu===
 
''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.
 
  
===Xuan Hien Nguyen===
+
== Abstracts ==
In the 1990's, Kapouleas and Traizet constructed new examples of minimal surfaces by desingularizing the intersection of existing ones, such as catenoids and planes, with Scherk surfaces. Using the same strategy, one can prove the existence of new self-translating and self-shrinking surfaces under mean curvature flow. In this talk, we will survey the results obtained so far and propose some generalization and simplification of the techniques.
 

Revision as of 11:40, 28 December 2014

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 Spring 2015

Seminar Schedule Spring 2015

date speaker title host(s)
January 26
February 2 Jessica Lin (Madison) TBA Kim
February 9
February 16
February 23 Jennifer Beichman (Madison) TBA Kim
March 2 Benoit Pausader (Princeton) TBA Kim
March 9
March 16
March 23
March 30 Spring recess Mar 28-Apr 5 (S-N)
April 6
April 13
April 20 Yuan Lou (Ohio State) TBA Zlatos
April 27
May 4


Abstracts