Fall 2021 and Spring 2022 Analysis Seminars: Difference between revisions

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'''Analysis Seminar
'''Analysis Seminar
'''
'''
[http://www.math.wisc.edu/~seeger/curr.html Current Semester]


The seminar will  meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
The seminar will  meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.


If you wish to invite a speaker please  contact  Andreas at seeger(at)math
If you wish to invite a speaker please  contact  Brian at street(at)math


===[[Previous Analysis seminars]]===
===[[Previous Analysis seminars]]===


= Analysis Seminar Schedule Spring 2017 =
= Analysis Seminar Schedule =
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
!align="left" | speaker
!align="left" | speaker
|align="left" | '''institution'''
!align="left" | title
!align="left" | title
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|January 17, Math Department  Colloquium
|Sept 11
| Fabio Pusateri (Princeton)
| Simon Marshall
|[[#Fabio Pusateri  |   The Water Waves Problem ]]
| Madison
| Angenent
|[[#Simon Marshall  | Integrals of eigenfunctions on hyperbolic manifolds ]]
|  
|-
|'''Wednesday, Sept 12'''
| Gunther Uhlmann 
| University of Washington
| Distinguished Lecture Series
| See colloquium website for location
|-
|'''Friday, Sept 14'''
| Gunther Uhlmann 
| University of Washington
| Distinguished Lecture Series
| See colloquium website for location
|-
|Sept 18
| Grad Student Seminar
|
|
|
|
|-
|-
|January 24, Joint Analysis/Geometry Seminar
|Sept 25
| Tamás Darvas (Maryland)
| Grad Student Seminar
|[[#Tamás Darvas  |  Existence of constant scalar curvature Kähler metrics and properness of the K-energy ]]
| Viaclovsky
|
|
|
|
|-
|Oct 2
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Oct 9
| Hong Wang
| MIT
|[[#linktoabstract  |  Title ]]
| Ruixiang
|-
|Oct 16
| Polona Durcik
| Caltech
|[[#linktoabstract  |  Title ]]
| Joris
|-
|Oct 23
| Song-Ying Li
| UC Irvine
|[[#linktoabstract  |  Title ]]
| Xianghong
|-
|Oct 30
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Nov 6
| Hanlong Fang
| UW Madison
|[[#linktoabstract  |  Title ]]
| Brian
|-
||'''Monday, Nov. 12'''
| Kyle Hambrook
| San Jose State University
|[[#linktoabstract  |  Title ]]
| Andreas
|-
|Nov 13
| Laurent Stolovitch
| Université de Nice - Sophia Antipolis
|[[#linktoabstract  |  Title ]]
|Xianghong
|-
|Dec 4
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Jan 22
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Jan 29
| Trevor Leslie
| UW Madison
|[[#linktoabstract  |  Title ]]
|
|-
|-
|Monday, January 30, 3:30, VV901 (PDE Seminar)
|Feb 5
| Serguei Denissov (UW Madison)
| No seminar
|[[#Serguei Denissov  | Instability in 2D Euler equation of incompressible inviscid fluid ]]
|  
|  
|
|
|-
|-
|February 7
|'''Friday, Feb 8'''
| Andreas Seeger (UW Madison)
| Aaron Naber
|[[#Andreas SeegerThe Haar system in Sobolev spaces]]
| Northwestern University
|[[#linktoabstract  Title ]]
| See colloquium website for location
|-
|Feb 12
| No seminar
|
|
|
|
|-
|-
|February 21
|'''Friday, Feb 15'''
| Jongchon Kim (UW Madison)
| Charles Smart
|[[#Jongchon Kim Some remarks on Fourier restriction estimates ]]
| University of Chicago
|[[#linktoabstract  |  Title ]]
| See colloquium website for information
|-
|Feb 19
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Feb 26
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Mar 5
| Person
| Institution
|[[#linktoabstract  Title ]]
| Sponsor
|-
|Mar 12
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Mar 19
|Spring Break!!!
|  
|  
|
|
|-
|-
|March 7, Mathematics Department Distinguished Lecture
|Apr 2
| Roger Temam (Indiana) 
| Person
|[[#Roger Temam (Colloquium) | On the mathematical  modeling of the humid atmosphere   ]]
| Institution
| Smith
|[[#linktoabstract Title ]]
| Sponsor
|-
|-
|Wednesday, March 8, Joint Applied Math/PDE/Analysis  Seminar
|Apr 9
| Roger Temam (Indiana) 
| Person
|[[#Roger Temam (Seminar) Weak solutions of the Shigesada-Kawasaki-Teramoto system]]
| Institution
| Smith
|[[#linktoabstract Title ]]
| Sponsor
|-
|-
|March 14
|Apr 9
| Xianghong Chen (UW Milwaukee)
| Person
|[[#Xianghong Chen  Restricting the Fourier transform to some oscillating curves ]]
| Institution
| Seeger
|[[#linktoabstract  Title ]]
|
| Sponsor
|-
|-
|March 21
|Apr 16
| SPRING BREAK
| Person
|[[#linktoabstract | ]]
| Institution
 
|[[#linktoabstract |   Title ]]
 
| Sponsor
|-
|-
|March 27 (joint PDE/Analysis seminar), 3:30, VV901
|Apr 23
| Sylvia Serfaty
| Person
|[[#linktoabstract |TBA ]]
| Institution
| Tran
|[[#linktoabstract |   Title ]]
|
| Sponsor
|-
|-
|March 28
|Apr 30
| Brian Cook (Fields Institute)
| Person
|[[#linktoabstract |TBA ]]
| Institution
| Seeger
|[[#linktoabstract |   Title ]]
|
| Sponsor
|-
|-
|April 4
| Francesco Di Plinio (Virginia)
|[[#linktoabstract  |  TBA ]]
| Seeger
|}
|}


=Abstracts=
=Abstracts=
===Simon Marshall===
''Integrals of eigenfunctions on hyperbolic manifolds''
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X.  I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity.  I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.


===   Fabio Pusateri  ===
===Name===
''The Water Waves problem''


We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.
Title


===  Tamás Darvas ===
Abstract
''Existence of constant scalar curvature Kähler metrics and properness of the K-energy''


Given a compact Kähler manifold $(X,\omega)$, we show that if there exists a constant
scalar curvature Kähler metric  cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an
appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful
study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is
joint work with Robert Berman and Chinh H. Lu.


=== Serguei Denissov  ===
===Name===
''Instability in 2D Euler equation of incompressible inviscid fluid''


We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.
Title


=== Andreas Seeger  ===
Abstract
''The Haar system in Sobolev spaces''


We consider the  Haar system on  Sobolev  spaces and ask:
When is it a Schauder basis?
When is it an unconditional  basis?
Some answers are given in recent joint work Tino Ullrich and Gustavo Garrigós.


=== Jongchon Kim  ===
===Name===
''Some remarks on Fourier restriction estimates''


The Fourier restriction problem, raised by Stein in the 1960’s, is a hard open problem in harmonic analysis. Recently, Guth made some impressive progress on this problem using polynomial partitioning, a divide and conquer technique developed by Guth and Katz for some problems in incidence geometry.
Title
In this talk, I will introduce the restriction problem and the polynomial partitioning method. In addition, I will present some sharp L^p to L^q estimates for the Fourier extension operator that use an estimate of Guth as a black box.


=== Roger Temam (Colloquium) ===
Abstract
''On the mathematical  modeling of the humid atmosphere''


The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase  due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.
=== Roger Temam (Seminar) ===
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''


We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.
===Name===
Based on an article with Du Pham, to appear in Nonlinear Analysis.


===  Xianghong Chen  ===
Title
''Restricting the Fourier transform to some oscillating curves''


I will talk about Fourier restriction to some compact smooth curves. The problem is relatively well understood for curves with nonvanishing torsion due to work of Drury from the 80's, but is less so for curves that contain 'flat' points (i.e. vanishing torsion). Sharp results are known for some monomial-like or finite type curves by work of Bak-Oberlin-Seeger, Dendrinos-Mueller, and Stovall, where a geometric inequality (among others) plays an important role. Such an inequality fails to hold if the torsion demonstrates strong sign-changing behavior, in which case endpoint restriction bounds may fail. In this talk I will present how one could obtain sharp non-endpoint results for certain space curves of this kind. Our approach uses a covering lemma for smooth functions that strengthens a variation bound of Sjolin, who used it to obtain a similar result for plane curves. This is joint work with Dashan Fan and Lifeng Wang.
Abstract


=Extras=
=Extras=
[[Blank Analysis Seminar Template]]
[[Blank Analysis Seminar Template]]

Revision as of 14:52, 11 September 2018

Analysis Seminar

The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.

If you wish to invite a speaker please contact Brian at street(at)math

Previous Analysis seminars

Analysis Seminar Schedule

date speaker institution title host(s)
Sept 11 Simon Marshall Madison Integrals of eigenfunctions on hyperbolic manifolds
Wednesday, Sept 12 Gunther Uhlmann University of Washington Distinguished Lecture Series See colloquium website for location
Friday, Sept 14 Gunther Uhlmann University of Washington Distinguished Lecture Series See colloquium website for location
Sept 18 Grad Student Seminar
Sept 25 Grad Student Seminar
Oct 2 Person Institution Title Sponsor
Oct 9 Hong Wang MIT Title Ruixiang
Oct 16 Polona Durcik Caltech Title Joris
Oct 23 Song-Ying Li UC Irvine Title Xianghong
Oct 30 Person Institution Title Sponsor
Nov 6 Hanlong Fang UW Madison Title Brian
Monday, Nov. 12 Kyle Hambrook San Jose State University Title Andreas
Nov 13 Laurent Stolovitch Université de Nice - Sophia Antipolis Title Xianghong
Dec 4 Person Institution Title Sponsor
Jan 22 Person Institution Title Sponsor
Jan 29 Trevor Leslie UW Madison Title
Feb 5 No seminar
Friday, Feb 8 Aaron Naber Northwestern University Title See colloquium website for location
Feb 12 No seminar
Friday, Feb 15 Charles Smart University of Chicago Title See colloquium website for information
Feb 19 Person Institution Title Sponsor
Feb 26 Person Institution Title Sponsor
Mar 5 Person Institution Title Sponsor
Mar 12 Person Institution Title Sponsor
Mar 19 Spring Break!!!
Apr 2 Person Institution Title Sponsor
Apr 9 Person Institution Title Sponsor
Apr 9 Person Institution Title Sponsor
Apr 16 Person Institution Title Sponsor
Apr 23 Person Institution Title Sponsor
Apr 30 Person Institution Title Sponsor

Abstracts

Simon Marshall

Integrals of eigenfunctions on hyperbolic manifolds

Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract

Extras

Blank Analysis Seminar Template