Difference between revisions of "Analysis Seminar"

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'''Fall 2019 and Spring 2020 Analysis Seminar Series
 
'''
 
  
The seminar will  meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
+
The 2020-2021 Analysis Seminar will be organized by David Beltran and Andreas Seeger.
 +
It will be online at least for the Fall semester, with details to be announced in September.
 +
The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier to accomodate speakers).
  
If you wish to invite a speaker please contact Brian at street(at)math
+
Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230
  
===[[Previous Analysis seminars]]===
+
If you'd like to suggest  speakers for the spring semester please contact David and Andreas (dbeltran at math, seeger at math).
  
= Analysis Seminar Schedule =
+
 
 +
 
 +
=[[Previous_Analysis_seminars]]=
 +
 
 +
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars
 +
 
 +
= Current Analysis Seminar Schedule =
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date   
 
!align="left" | date   
Line 16: Line 22:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|Sept 10
+
|September 22
| José Madrid
+
|Alexei Poltoratski
| UCLA
+
|UW Madison
|[[#José Madrid  |  On the regularity of maximal operators on Sobolev Spaces ]]
+
|[[#Alexei Poltoratski Dirac inner functions ]]
| Andreas, David
 
|-
 
|Sept 13 (Friday, B139)
 
| Yakun Xi
 
| University of  Rochester
 
|[[#Yakun Xi  |  Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]
 
| Shaoming
 
|-
 
|Sept 17
 
| Joris Roos
 
| UW Madison
 
|[[#Joris Roos  |  L^p improving estimates for maximal spherical averages ]]
 
| Brian
 
|-
 
|Sept 20 (2:25 PM Friday, Room B139 VV)
 
| Xiaojun Huang
 
| Rutgers University–New Brunswick
 
|[[#linktoabstract  |  A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]
 
| Xianghong
 
|-
 
|Sept 24
 
| Person
 
| Institution
 
|[[#linktoabstract  |  Title ]]
 
| Sponsor
 
|-
 
|Oct 1
 
| Xiaocheng Li
 
| UW Madison
 
|[[#Xiaocheng Li  |  An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]
 
| Simon
 
|-
 
|Oct 8
 
| Jeff Galkowski
 
| Northeastern University
 
|[[#Jeff Galkowski  |  Concentration and Growth of Laplace Eigenfunctions ]]
 
| Betsy
 
|-
 
|Oct 15
 
| David Beltran
 
| UW Madison
 
|[[#David Beltran  |  Regularity of the centered fractional maximal function ]]
 
| Brian
 
|-
 
|Oct 22
 
| Laurent Stolovitch
 
| University of Nice Sophia-Antipolis
 
|[[#linktoabstract  |  Title ]]
 
| Xianghong
 
|-
 
|<b>Wednesday Oct 23 in B129</b>
 
|Dominique Kemp
 
|Indiana University
 
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]
 
|Betsy
 
|-
 
|Oct 29
 
| Bingyang Hu
 
| UW Madison
 
|[[#linktoabstract  |  Title ]]
 
| Street
 
|-
 
|Nov 5
 
| Kevin O'Neill
 
| UC Davis
 
|[[#Kevin O'Neill  |  A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]
 
| Betsy
 
|-
 
|Nov 12
 
| Francesco di Plinio
 
| Washington University in St. Louis
 
|[[#linktoabstract  |  Title ]]
 
| Shaoming
 
|-
 
|Nov 19
 
| Joao Ramos
 
| University of Bonn
 
|[[#linktoabstract Title ]]
 
| Joris, Shaoming
 
|-
 
|Nov 26
 
| No Seminar
 
 
|  
 
|  
|
 
|
 
|-
 
|Dec 3
 
| Person
 
| Institution
 
|[[#linktoabstract  |  Title ]]
 
| Sponsor
 
 
|-
 
|-
|Dec 10
+
|September 29
| No Seminar
+
|Polona Durcik
 +
| Chapman University
 +
|[[#Polona Durcik and Joris Rooslinktoabstract  |  A triangular Hilbert transform with curvature, I ]]
 
|  
 
|  
|
 
|
 
 
|-
 
|-
|Jan 21
+
|Wednesday September 30, 4 p.m.
| No Seminar
+
|Joris Roos
 +
|University of Massachusetts - Lowell
 +
|[[#Polona Durcik and Joris Roos  |  A triangular Hilbert transform with curvature, II ]]
 
|  
 
|  
|
 
|
 
 
|-
 
|-
|Jan 28
+
|October 6
| Person
+
|Andrew Zimmer
| Institution
+
|UW Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Feb 4
+
|October 13
| Person
+
|Hong Wang
| Institution
+
|Princeton/IAS
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Feb 11
+
|October 20
| Person
+
|Kevin Luli
| Institution
+
|UC Davis
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Feb 18
+
|October 27
| Person
+
|Terence Harris
| Institution
+
| Cornell University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Feb 25
+
|Monday, November 2, 4 p.m.
| Person
+
|Yuval Wigderson
| Institution
+
|Stanford  University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Mar 3
+
|November 10
| Person
+
|Óscar Domínguez
| Institution
+
| Universidad Complutense de Madrid
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Mar 10
+
|November 17
| Person
+
|Tamas Titkos
| Institution
+
|BBS U of Applied Sciences and Renyi Institute
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Mar 17
+
|November 24
| Spring Break!
+
|Shukun Wu
|
+
|University of Illinois (Urbana-Champaign)
|
+
||[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|Mar 24
+
|December 1
| Oscar Dominguez
+
| Jonathan Hickman
| Universidad Complutense de Madrid
+
| The University of Edinburgh
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|  
 
|-
 
|-
|Mar 31
+
|December 8
| Reserved
+
|TBA
| Institution
+
|  
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Street
+
|  
 
|-
 
|-
|Apr 7
+
|February 2
| Hong Wang
+
|Jongchon Kim
| Institution
+
| UBC
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Street
+
|  
 
|-
 
|-
|Apr 14
+
|February 9
| Person
+
|Bingyang Hu
| Institution
+
|Purdue University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Apr 21
+
|February 16
| Diogo Oliveira e Silva
+
|David Beltran
| University of Birmingham
+
|UW - Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
 
|-
 
|Apr 28
 
| No Seminar
 
|-
 
|May 5
 
|Jonathan Hickman
 
|University of Edinburgh
 
|[[#linktoabstract  |  Title ]]
 
| Andreas
 
|-
 
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===José Madrid===
+
===Alexei Poltoratski===
  
Title: On the regularity of maximal operators on Sobolev Spaces
+
Title: Dirac inner functions
  
Abstract: In this talk, we will discuss the regularity properties (boundedness and
+
Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations.
continuity) of the classical and fractional maximal
+
We will discuss connections between problems in complex function theory, spectral and scattering problems for differential
operators when these act on the Sobolev space W^{1,p}(\R^n). We will
+
operators and the non-linear Fourier transform.
focus on the endpoint case p=1. We will talk about
 
some recent results and current open problems.
 
  
===Yakun Xi===
 
  
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities
+
===Polona Durcik and Joris Roos===
  
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.
+
Title: A triangular Hilbert transform with curvature
  
===Joris Roos===
+
Abstract: The triangular Hilbert is a two-dimensional bilinear singular
 +
originating in time-frequency analysis. No Lp bounds are currently
 +
known for this operator.
 +
In these two talks we discuss a recent joint work with Michael Christ
 +
on a variant of the triangular Hilbert transform involving curvature.
 +
This object is closely related to the bilinear Hilbert transform with
 +
curvature and a maximally modulated singular integral of Stein-Wainger
 +
type. As an application we also discuss a quantitative nonlinear Roth
 +
type theorem on patterns in the Euclidean plane.
 +
The second talk will focus on the proof of a key ingredient, a certain
 +
regularity estimate for a local operator.
  
Title: L^p improving estimates for maximal spherical averages
+
===Name===
  
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.
+
Title
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.
 
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.
 
  
===Xiaojun Huang===
+
Abstract
  
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries
 
  
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.
+
===Name===
  
 +
Title
  
 +
Abstract
  
  
===Xiaocheng Li===
+
===Name===
  
Title:  An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$
+
Title
  
Abstract:  We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.
+
Abstract
  
===Jeff Galkowski===
+
=Extras=
 
+
[[Blank Analysis Seminar Template]]
<b>Concentration and Growth of Laplace Eigenfunctions</b>
 
 
 
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.
 
 
 
===David Beltran===
 
 
 
Title: Regularity of the centered fractional maximal function
 
 
 
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.
 
 
 
This is joint work with José Madrid.
 
 
 
===Dominique Kemp===
 
 
 
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b>
 
 
 
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone.  Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.
 
  
  
===Kevin O'Neill===
+
Graduate Student Seminar:
  
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b>
+
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
 
 
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.
 
 
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 

Latest revision as of 18:14, 21 September 2020

The 2020-2021 Analysis Seminar will be organized by David Beltran and Andreas Seeger. It will be online at least for the Fall semester, with details to be announced in September. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier to accomodate speakers).

Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230

If you'd like to suggest speakers for the spring semester please contact David and Andreas (dbeltran at math, seeger at math).


Previous_Analysis_seminars

https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars

Current Analysis Seminar Schedule

date speaker institution title host(s)
September 22 Alexei Poltoratski UW Madison Dirac inner functions
September 29 Polona Durcik Chapman University A triangular Hilbert transform with curvature, I
Wednesday September 30, 4 p.m. Joris Roos University of Massachusetts - Lowell A triangular Hilbert transform with curvature, II
October 6 Andrew Zimmer UW Madison Title
October 13 Hong Wang Princeton/IAS Title
October 20 Kevin Luli UC Davis Title
October 27 Terence Harris Cornell University Title
Monday, November 2, 4 p.m. Yuval Wigderson Stanford University Title
November 10 Óscar Domínguez Universidad Complutense de Madrid Title
November 17 Tamas Titkos BBS U of Applied Sciences and Renyi Institute Title
November 24 Shukun Wu University of Illinois (Urbana-Champaign) Title
December 1 Jonathan Hickman The University of Edinburgh Title
December 8 TBA Title
February 2 Jongchon Kim UBC Title
February 9 Bingyang Hu Purdue University Title
February 16 David Beltran UW - Madison Title

Abstracts

Alexei Poltoratski

Title: Dirac inner functions

Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations. We will discuss connections between problems in complex function theory, spectral and scattering problems for differential operators and the non-linear Fourier transform.


Polona Durcik and Joris Roos

Title: A triangular Hilbert transform with curvature

Abstract: The triangular Hilbert is a two-dimensional bilinear singular originating in time-frequency analysis. No Lp bounds are currently known for this operator. In these two talks we discuss a recent joint work with Michael Christ on a variant of the triangular Hilbert transform involving curvature. This object is closely related to the bilinear Hilbert transform with curvature and a maximally modulated singular integral of Stein-Wainger type. As an application we also discuss a quantitative nonlinear Roth type theorem on patterns in the Euclidean plane. The second talk will focus on the proof of a key ingredient, a certain regularity estimate for a local operator.

Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract

Extras

Blank Analysis Seminar Template


Graduate Student Seminar:

https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html