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
| Sigurd 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 ]]
| Jeff 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, January 30, 3:30, VV901 (PDE Seminar)
||'''Monday, Nov. 12'''
| Serguei Denissov (UW Madison)
| Kyle Hambrook
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid ]]
| San Jose State University
|  
|[[#linktoabstract |   Title ]]
| Andreas
|-
|-
|February 7
|Nov 13
| Andreas Seeger (UW Madison)
| Laurent Stolovitch
|[[#Andreas SeegerThe Haar system in Sobolev spaces]]
| Université de Nice - Sophia Antipolis
|
|[[#linktoabstract  Title ]]
|Xianghong
|-
|-
|February 21
|Dec 4
| Jongchon Kim (UW Madison)
| Person
|[[#Jongchon Kim Some remarks on Fourier restriction estimates ]]
| Institution
| Andreas Seeger
|[[#linktoabstract  Title ]]
| Sponsor
|-
|-
|March 7, Mathematics Department Distinguished Lecture
|Jan 22
| Roger Temam (Indiana) 
| Person
|[[#Roger Temam (Colloquium) | On the mathematical  modeling of the humid atmosphere   ]]
| Institution
| Leslie Smith
|[[#linktoabstract Title ]]
| Sponsor
|-
|-
|Wednesday, March 8, Joint Applied Math/PDE/Analysis  Seminar
|Jan 29
| Roger Temam (Indiana) 
| Trevor Leslie
|[[#Roger Temam (Seminar) Weak solutions of the Shigesada-Kawasaki-Teramoto system]]
| UW Madison
| Leslie Smith
|[[#linktoabstract Title ]]
|  
|-
|-
|March 14
|Feb 5
| Xianghong Chen (UW Milwaukee)
| No seminar
|[[#Xianghong Chen  |  Restricting the Fourier transform to some oscillating curves ]]
|  
| Andreas Seeger
|
|
|
|-
|-
|March 21
|'''Friday, Feb 8'''
| SPRING BREAK
| Aaron Naber
|[[#linktoabstract | ]]
| Northwestern University
 
|[[#linktoabstract |   Title ]]
 
| See colloquium website for location
|-
|-
|Monday, March 27 (joint PDE/Analysis Seminar), 3:30, VV901
|Feb 12
| Sylvia Serfaty (NYU)
| No seminar
|[[#Sylvia Serfaty |Mean Field Limits for Ginzburg Landau Vortices ]]
|
| Hung Tran
|
|
|
|-
|-
|March 28
|'''Friday, Feb 15'''
| Brian Cook (Fields Institute)
| Charles Smart
|[[#Brian Cook |Twists on the twisted ergodic theorems ]]
| University of Chicago
| Andreas Seeger
|[[#linktoabstract  |  Title ]]
|
| See colloquium website for information
|-
|Feb 19
| Person
| Institution
|[[#linktoabstract  |   Title ]]
| Sponsor
|-
|Feb 26
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|-
|Friday, March 31, 4:00 p.m., B139
|Mar 5
| Laura Cladek (UBC)
| Person
|[[#Laura Cladek | Endpoint bounds for the lacunary spherical maximal operator ]]
| Institution
| Andreas Seeger
|[[#linktoabstract  |   Title ]]
|
| Sponsor
|-
|-
|April 4
|Mar 12
| Francesco Di Plinio (Virginia)
| Person
|[[#Francesco di Plinio Sparse domination of singular integral operators ]]
| Institution
| Andreas Seeger
|[[#linktoabstract  Title ]]
|
| Sponsor
|-
|-
|April 11
|Mar 19
| Xianghong Gong (UW Madison)
|Spring Break!!!
|[[#lXianghong Gong |  Hoelder estimates for homotopy operators on strictly pseudoconvex domains with C^2 boundary ]]
|  
|  
|
|
|
|-
|-
|April 25 (joint PDE/Analysis Seminar)
|Apr 2
| Chris Henderson (University of Chicago)
| Person
|[[#lChris Henderson A local-in-time Harnack inequality and applications to reaction-diffusion equations ]]
| Institution
| Jessica Lin
|[[#linktoabstract  Title ]]
|
| Sponsor
|-}
|-
|Apr 9
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Apr 9
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Apr 16
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Apr 23
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Apr 30
| Person
| Institution
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|}


=Abstracts=
=Abstracts=
===Simon Marshall===


===  Fabio Pusateri  ===
''Integrals of eigenfunctions on hyperbolic manifolds''
''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.
 
===  Tamás Darvas ===
''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  ===
''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.
 
=== Andreas Seeger  ===
''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  ===
''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.
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) ===
''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.
Based on an article with Du Pham, to appear in Nonlinear Analysis.
 
===  Xianghong Chen  ===
''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.
 
===Sylvia Serfaty ===


''Mean Field Limits for Ginzburg Landau Vortices''
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.


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.


===Name===


Title


=== Brian Cook ===
Abstract
''Twists on the twisted ergodic theorems''


The classical pointwise ergodic theorem has been adapted to include averages twisted by a phase polynomial, primary examples being the ergodic theorems of Wiener-Wintner and Lesigne. Certain uniform versions of these results are also known. Here uniformity refers to the collection of polynomials of degree less than some prescribed number. In this talk we wish to consider weakening the hypothesis in these latter results by considering uniformity over a smaller class of polynomials, which is naturally motivated when considering certain applications related to the circle method.


===Name===


=== Laura Cladek ===
Title
''Endpoint bounds for the lacunary spherical maximal operator''


Define the lacunary spherical maximal operator as the maximal operator corresponding to averages over spheres of radius 2^k for k an integer. This operator may be viewed as a model case for studying more general classes of singular maximal operators and Radon transforms. It is a classical result in harmonic analysis that this operator is bounded on L^p for p>1, but the question of weak-type (1, 1) boundedness (which would correspond to pointwise convergence of lacunary spherical averages for functions in L^1 has remained open. Although this question still remains open, we discuss some new endpoint bounds for the operator near L^1 that allows us to conclude almost everywhere pointwise convergence of lacunary spherical means for functions in a slightly smaller space than L\log\log\log L. This is based on joint work with Ben Krause.
Abstract




=== Francesco di Plinio ===
===Name===
''Sparse domination of singular integral operators''


Singular integral operators, which are a priori signed and non-local, can be dominated  in norm, pointwise, or dually, by sparse averaging operators,  which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather immediate estimates for the averaging operators.  In this talk, we present several positive sparse domination results of singular integrals falling beyond the scope of classical Calderón-Zygmund theory; notably, modulation invariant multilinear singular integrals including the bilinear Hilbert transforms, variation norm Carleson operators, matrix-valued kernels, rough homogeneous singular integrals and critical Bochner-Riesz means, and singular integrals along submanifolds with curvature.  Collaborators:  Amalia Culiuc, Laura Cladek, Jose Manuel Conde-Alonso, Yen Do, Yumeng Ou and Gennady Uraltsev.
Title


Abstract


===Xianghong Gong===
''Hoelder estimates for homotopy operators on strictly pseudoconvex domains with C^2 boundary''


Abstract: We derive a new homotopy formula for a bounded strictly pseudoconvex domain of C^2 boundary by using a method of Lieb and Range,  and we obtain estimates for its homotopy operator. We show that the d-bar equation on the domain admits a solution gaining half-derivative in the Hoelder-Zygmund spaces. The estimates are also applied to obtain a boundary regularity for D-solutions on a suitable product domain in the Levi-flat Euclidean spaces.
===Name===


===Chris Henderson===
Title
''A local-in-time Harnack inequality and applications to reaction-diffusion equations''


Abstract: The classical Harnack inequality requires one to look back in time to obtain a uniform lower bound on the solution to a parabolic equation.  In this talk, I will introduce a Harnack-type inequality that allows us to remove this restriction at the expense of a slightly weaker bound.  I will then discuss applications of this bound to (time permitting) three non-local reaction-diffusion equations arising in biology.  In particular, in each case, this inequality allows us to show that solutions to these equations, which do not enjoy a maximum principle, may be compared with solutions to a related local equation, which does enjoy a maximum principle.  Precise estimates of the propagation speed follow from this.
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