Difference between revisions of "Analysis Seminar"

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'''Analysis Seminar
 
'''
 
  
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 Betsy at stovall(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).
  
= Summer/Fall 2017 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)
 
|-
 
|-
|September 8 in B239
+
|September 22
| Tess Anderson
+
|Alexei Poltoratski
| UW Madison
+
|UW Madison
 +
|[[#Alexei Poltoratski  |  Dirac inner functions ]]
 +
|
 +
|-
 +
|September 29
 +
|Joris Roos
 +
|University of Massachusetts - Lowell
 +
|[[#Polona Durcik and Joris Rooslinktoabstract  |  A triangular Hilbert transform with curvature, I ]]
 +
|
 +
|-
 +
|Wednesday September 30, 4 p.m.
 +
|Polona Durcik
 +
|Chapman University
 +
|[[#Polona Durcik and Joris Roos  |  A triangular Hilbert transform with curvature, II ]]
 +
|
 +
|-
 +
|October 6
 +
|Andrew Zimmer
 +
|UW Madison
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|October 13
 +
|Hong Wang
 +
|Princeton/IAS
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|October 20
 +
|Kevin Luli
 +
|UC Davis
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
|
+
|
 +
|-
 +
|October 27
 +
|Terence Harris
 +
| Cornell University
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|Monday, November 2, 4 p.m.
 +
|Yuval Wigderson
 +
|Stanford  University
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|November 10
 +
|Óscar Domínguez
 +
| Universidad Complutense de Madrid
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|November 17
 +
|Tamas Titkos
 +
|BBS U of Applied Sciences and Renyi Institute
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|November 24
 +
|Shukun Wu
 +
|University of Illinois (Urbana-Champaign)
 +
||[[#linktoabstract  |  Title ]]
 +
|  
 
|-
 
|-
|September 12
+
|December 1
 +
| Jonathan Hickman
 +
| The University of Edinburgh
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 +
|-
 +
|December 8
 +
|TBA
 
|  
 
|  
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|September 19
+
|February 2
| Brian Street
+
|Jongchon Kim
| UW Madison
+
| UBC
|[[#Brian Street Convenient Coordinates ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
|
 +
|-
 +
|February 9
 +
|Bingyang Hu
 +
|Purdue University
 +
|[[#linktoabstract  |  Title ]]
 +
|  
 
|-
 
|-
|September 26
+
|February 16
| Hiroyoshi Mitake
+
|David Beltran
| Hiroshima University
+
|UW - Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Hung
+
|
 
|-
 
|-
|October 3
+
|February 23
| Joris Roos
+
|
| UW Madison
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|October 10
+
|March 2
| Michael Greenblatt
+
|
| UI Chicago
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|
 
|-
 
|-
|October 17
+
|March 9
| David Beltran
+
|
| Bilbao
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|
 
|-
 
|-
|October 24
+
|March 16
| Xiaochun Li
+
|Ziming Shi
| UIUC
+
|Rutgers University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|Thursday, October 26
+
|March 23
| Fedya Nazarov
+
|
| Kent State University
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy, Andreas
+
|
 
|-
 
|-
|Friday, October 27 in B239
+
|March 30
| Stefanie Petermichl
+
|
| University of Toulouse
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy, Andreas
+
|
 
|-
 
|-
|November 14
+
|April 6
| Naser Talebizadeh Sardari
+
|
| UW Madison
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|November 28
+
|April 13
| Xianghong Chen
+
|
| UW Milwaukee
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|December 5
+
|April 20
 
|
 
|
 
|
 
|
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|
 
|
 
|-
 
|-
|December 12
+
|April 27
| Alex Stokolos
+
|
| GA Southern
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|
 
|-
 
|-
 +
|May 4
 +
|
 +
|
 +
|[[#linktoabstract  |  Title ]]
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Brian Street===
+
===Alexei Poltoratski===
  
Title: Convenient Coordinates
+
Title: Dirac inner functions
  
Abstract: We discuss the method of picking a convenient coordinate system adapted to vector fields. Let X_1,...,X_q be either real or complex C^1 vector fields.  We discuss the question of when there is a coordinate system in which the vector fields are smoother (e.g., C^m, or C^\infty, or real analytic).  By answering this in a quantitative way, we obtain coordinate charts which can be used as generalized scaling maps.  When the vector fields are real this is joint work with Stovall, and continues in the line of quantitative sub-Riemannian geometry initiated by Nagel, Stein, and Wainger.  When the vector fields are complex one obtains a geometry with more structure which can be thought of as "sub-Hermitian".
+
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===
 
===Name===
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Abstract
 
Abstract
  
 
===Naser Talebizadeh Sardari===
 
 
Quadratic forms and the semiclassical eigenfunction hypothesis
 
 
Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math>k</math> variables, where <math>k\geq4</math>,  and discriminant <math>D</math>. For any integer <math>n</math>, we give an upper bound on the number of integral solutions of <math>Q(X)=n</math>  in terms of <math>n</math>, <math>k</math>, and <math>D</math>. As a corollary, we prove  a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given  eigenspace of the Laplacian on the flat torus <math>\mathbb{T}^d</math> for <math>d\geq 5</math>. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.
 
  
 
===Name===
 
===Name===
Line 135: Line 229:
  
 
Abstract
 
Abstract
 
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]
 +
 +
 +
Graduate Student Seminar:
 +
 +
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html

Latest revision as of 14:47, 28 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 Joris Roos University of Massachusetts - Lowell A triangular Hilbert transform with curvature, I
Wednesday September 30, 4 p.m. Polona Durcik Chapman University 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