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, or on different days, 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)
+
|September 29
| Yakun Xi
+
|Polona Durcik
| University of  Rochester
+
| Chapman University
|[[#Yakun Xi |   Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]
+
|[[#Polona Durcik and Joris Rooslinktoabstract | A triangular Hilbert transform with curvature, I ]]
| Shaoming
+
|  
 
|-
 
|-
|Sept 17
+
|Wednesday September 30, 4 p.m.
| Joris Roos
+
|Joris Roos
| UW Madison
+
|University of Massachusetts - Lowell
|[[#Joris Roos  |   L^p improving estimates for maximal spherical averages ]]
+
|[[#Polona Durcik and Joris Roos  | A triangular Hilbert transform with curvature, II ]]
| Brian
+
|  
 
|-
 
|-
|Sept 20 (2:25 PM Friday, Room B139 VV)
+
|October 6
| Xiaojun Huang
+
|Andrew Zimmer
| Rutgers University–New Brunswick
+
|UW Madison
|[[#linktoabstract  |  A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]
+
|[[#linktoabstract  |  Title ]]
| Xianghong
+
|  
 
|-
 
|-
|Oct 1
+
|October 13
| Xiaocheng Li
+
|Hong Wang
| UW Madison
+
|Princeton/IAS
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]
+
|[[#linktoabstract |   Title ]]
| Simon
+
|  
 
|-
 
|-
|Oct 8
+
|October 20
| Jeff Galkowski
+
|Kevin Luli
| Northeastern University
+
|UC Davis
|[[#Jeff Galkowski Concentration and Growth of Laplace Eigenfunctions ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
|  
 
|-
 
|-
|Oct 15
+
|October 27
| David Beltran
+
|Terence Harris
| UW Madison
+
| Cornell University
|[[#David Beltran Regularity of the centered fractional maximal function ]]
+
|[[#linktoabstract Title ]]
| Brian
+
|  
 
|-
 
|-
|Oct 22
+
|Monday, November 2, 4 p.m.
| Laurent Stolovitch
+
|Yuval Wigderson
| University of Côte d'Azur
+
|Stanford  University
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]
+
|[[#linktoabstract |   Title ]]
| Xianghong
+
|  
 
|-
 
|-
|<b>Wednesday Oct 23 in B129</b>
+
|November 10
|Dominique Kemp
+
|Óscar Domínguez
|Indiana University
+
| Universidad Complutense de Madrid
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]
+
|[[#linktoabstract  |   Title ]]
|Betsy
+
|  
 
|-
 
|-
|Oct 29
+
|November 17
| Bingyang Hu
+
|Tamas Titkos
| UW Madison
+
|BBS U of Applied Sciences and Renyi Institute
|[[#Bingyang Hu |   Sparse bounds of singular Radon transforms]]
+
|[[#linktoabstract |   Title ]]
| Street
+
|  
 
|-
 
|-
|Nov 5
+
|November 24
| Kevin O'Neill
+
|Shukun Wu
| UC Davis
+
|University of Illinois (Urbana-Champaign)
|[[#Kevin O'Neill A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]
+
||[[#linktoabstract Title ]]  
| Betsy
+
|  
 
|-
 
|-
|Nov 12
+
|December 1
| Francesco di Plinio
+
| Jonathan Hickman
| Washington University in St. Louis
+
| The University of Edinburgh
|[[#Francesco di Plinio Maximal directional integrals along algebraic and lacunary sets]]
+
|[[#linktoabstract Title ]]
| Shaoming
+
|  
 
|-
 
|-
|Nov 13 (Wednesday)
+
|December 8
| Xiaochun Li
+
|TBA
| UIUC
 
|[[#Xiaochun Li  |  Roth's type theorems on progressions]]
 
| Brian, Shaoming
 
|-
 
|Nov 19
 
| Joao Ramos
 
| University of Bonn
 
|[[#Joao Ramos  |  Fourier uncertainty principles, interpolation and uniqueness sets ]]
 
| Joris, Shaoming
 
|-
 
|Nov 26
 
| No Seminar
 
 
|  
 
|  
|
+
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|Dec 3
+
|February 2
| Person
+
|Jongchon Kim
| Institution
+
| UBC
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Dec 10
+
|February 9
| No Seminar
+
|Bingyang Hu
 +
|Purdue University
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
+
|-
 +
|February 16
 +
|David Beltran
 +
|UW - Madison
 +
|[[#linktoabstract  |  Title ]]
 
|
 
|
 
|-
 
|-
|Jan 21
+
|February 23
| No Seminar
 
|
 
 
|
 
|
 
|
 
|
|-
 
|Jan 28
 
| Person
 
| Institution
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|
 
|-
 
|-
|Feb 4
+
|March 2
| Person
+
|
| Institution
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|
 
|-
 
|-
|Feb 11
+
|March 9
| Person
+
|
| Institution
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|
 
|-
 
|-
|Feb 18
+
|March 16
| Sergey Denisov
+
|Ziming Shi
| UW Madison
+
|Rutgers University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Street
+
|
 
|-
 
|-
|Feb 25
+
|March 23
| Dmitry Chelkak
+
|
| Ecole Normale, Paris
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Denisov
+
|
 
|-
 
|-
|Mar 3
+
|March 30
| William Green
+
|
| Rose-Hulman Institute of Technology
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|Mar 10
+
|April 6
| Yifei Pan
+
|
| Indiana University-Purdue University Fort Wayne
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong
+
|
 
|-
 
|-
|Mar 17
+
|April 13
| Spring Break!
 
 
|
 
|
 
|
 
|
|
 
|-
 
|Mar 24
 
| Oscar Dominguez
 
| Universidad Complutense de Madrid
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|
 
|-
 
|-
|Mar 31
+
|April 20
| Reserved
+
|
| Institution
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Street
+
|
 
|-
 
|-
|Apr 7
+
|April 27
| Hong Wang
+
|
| Institution
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Street
+
|
 
|-
 
|-
|<b>Monday, Apr 13</b>
+
|May 4
|Yumeng Ou
+
|
|CUNY, Baruch College
+
|
|[[#linktoabstract  |  TBA ]]
 
|Zhang
 
|-
 
|Apr 14
 
| Tamás Titkos
 
| BBS University of Applied Sciences & Rényi Institute
 
|[[#linktoabstract  |  Distance preserving maps on spaces of probability measures ]]
 
| Street
 
|-
 
|Apr 21
 
| Diogo Oliveira e Silva
 
| University of Birmingham
 
 
|[[#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, I & II.
  
===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.
 
  
 +
Abstract
  
  
===Joao Ramos===
+
===Name===
  
Title: Fourier uncertainty principles, interpolation and uniqueness sets
+
Title
  
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that
+
Abstract
  
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$
 
  
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers.
+
===Name===
  
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$
+
Title
  
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.
+
Abstract
  
===Xiaojun Huang===
+
=Extras=
 
+
[[Blank Analysis Seminar Template]]
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.
 
 
 
===Xiaocheng Li===
 
 
 
Title:  An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$
 
 
 
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.
 
 
 
 
 
===Xiaochun Li===
 
 
 
Title:  Roth’s type theorems on progressions
 
 
 
Abstract:  The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.
 
 
 
===Jeff Galkowski===
 
 
 
<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===
 
 
 
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b>
 
 
 
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.
 
 
 
 
 
 
 
===Francesco di Plinio===
 
 
 
<b>Maximal directional integrals along algebraic and lacunary sets </b>
 
 
 
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas  of Parcet-Rogers and of  Nagel-Stein-Wainger.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
===Laurent Stolovitch===
 
 
 
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b>
 
 
 
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.
 
  
  
===Bingyang Hu===
+
Graduate Student Seminar:
  
<b>Sparse bounds of singular Radon transforms</b>
+
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
 
 
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.
 
 
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 

Latest revision as of 13:22, 25 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, or on different days, 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
February 23 Title
March 2 Title
March 9 Title
March 16 Ziming Shi Rutgers University Title
March 23 Title
March 30 Title
April 6 Title
April 13 Title
April 20 Title
April 27 Title
May 4 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, I & II.

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