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
 +
|[[#Andrew Zimmer  |  Complex analytic problems on domains with good intrinsic geometry ]]
 +
|
 +
|-
 +
|October 13
 +
|Hong Wang
 +
|Princeton/IAS
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|October 20
 +
|Kevin Luli
 +
|UC Davis
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
|
+
|  
 
|-
 
|-
|September 12
+
|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 ]]
 
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|September 19
+
|November 24
| Brian Street
+
|Shukun Wu
| UW Madison
+
|University of Illinois (Urbana-Champaign)
|[[#Brian Street Convenient Coordinates ]]
+
||[[#linktoabstract  |  Title ]]
| Betsy
+
|
 +
|-
 +
|December 1
 +
| Jonathan Hickman
 +
| The University of Edinburgh
 +
|[[#linktoabstract Title ]]
 +
|  
 
|-
 
|-
|September 26
+
|December 8
| Hiroyoshi Mitake
+
|Alejandra Gaitán
| Hiroshima University
+
| Purdue University
|[[#Hiroyoshi Mitake Derivation of multi-layered interface system and its application ]]
+
|[[#linktoabstract Title ]]
| Hung
+
|  
 
|-
 
|-
|October 3
+
|February 2
| Joris Roos
+
|Jongchon Kim
| UW Madison
+
| UBC
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|  
 
|-
 
|-
|October 10
+
|February 9
| Michael Greenblatt
+
|Bingyang Hu
| UI Chicago
+
|Purdue University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|  
 
|-
 
|-
|October 17
+
|February 16
| David Beltran
+
|David Beltran
| Bilbao
+
|UW - Madison
|[[#David Beltran Fefferman-Stein inequalities ]]
+
|[[#linktoabstract Title ]]
| Andreas
+
|
 
|-
 
|-
|October 24
+
|February 23
| Xiaochun Li
+
|
| UIUC
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|Thursday, October 26
+
|March 2
| Fedya Nazarov
+
|
| Kent State University
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy, Andreas
+
|
 
|-
 
|-
|Friday, October 27 in B239
+
|March 9
| Stefanie Petermichl
+
|
| University of Toulouse
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy, Andreas
+
|
 
|-
 
|-
|November 14
+
|March 16
| Naser Talebizadeh Sardari
+
|Ziming Shi
| UW Madison
+
|Rutgers University
|[[#linktoabstract  |  Quadratic forms and the semiclassical eigenfunction hypothesis ]]
+
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|November 28
+
|March 23
| Xianghong Chen
+
|
| UW Milwaukee
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|
 
|-
 
|-
|December 5
+
|March 30
 
|
 
|
 
|
 
|
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|
 
|
 
|-
 
|-
|December 12
+
|April 6
| Alex Stokolos
+
|
| GA Southern
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
|
 
|-
 
|-
 +
|April 13
 +
|
 +
|
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|April 20
 +
|
 +
|
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|April 27
 +
|
 +
|
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|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.
  
  
===Hiroyoshi Mitake===
+
===Polona Durcik and Joris Roos===
  
Title: Derivation of multi-layered interface system and its application
+
Title: A triangular Hilbert transform with curvature, I & II.
  
Abstract:   In this talk, I will propose a multi-layered interface system which can
+
Abstract: The triangular Hilbert is a two-dimensional bilinear singular
be formally derived by the singular limit of the weakly coupled system of
+
originating in time-frequency analysis. No Lp bounds are currently
the Allen-Cahn equation. By using the level set approach, this system can be
+
known for this operator.
written as a quasi-monotone degenerate parabolic system.
+
In these two talks we discuss a recent joint work with Michael Christ
We give results of the well-posedness of viscosity solutions, and study the  
+
on a variant of the triangular Hilbert transform involving curvature.
singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.
+
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.
  
 +
===Andrew Zimmer===
  
===David Beltran===
+
Title:  Complex analytic problems on domains with good intrinsic geometry
  
Fefferman Stein Inequalities
+
Abstract: In this talk, I will describe a new class of domains in complex Euclidean space which is defined in terms of the existence of a Kaehler metric with good geometric properties. This class is invariant under biholomorphism and includes many well-studied classes of domains such as strongly pseudoconvex domains, finite type domains in dimension two, convex domains, homogeneous domains, and embeddings of Teichmuller spaces. Further, certain analytic problems are tractable for domains in this family even when the boundary is non-smooth. In particular, it is possible to characterize the domains in this family where the dbar-Neumann operator on (0, q)-forms is compact (which generalizes an old result of Fu-Straube for convex domains).
  
Given an operator T, we focus on obtaining two-weighted inequalities in which the weights are related via certain maximal function. These inequalites, which originated in work of Fefferman and Stein, have been established in an optimal way for different classical operators in Harmonic Analysis. In this talk, we survey some classical results and we present some recent Fefferman-Stein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.
+
===Name===
  
 +
Title
  
 +
Abstract
  
===Naser Talebizadeh Sardari===
+
===Name===
 +
 
 +
Title
  
Quadratic forms and the semiclassical eigenfunction hypothesis
+
Abstract
  
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===
 +
 
 +
Title
 +
 
 +
Abstract
 +
 
 +
===Name===
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 +
Title
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Abstract
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===Name===
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Title
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Abstract
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===Name===
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Title
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Abstract
  
 
===Name===
 
===Name===
Line 144: Line 261:
 
=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 20:43, 30 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 Complex analytic problems on domains with good intrinsic geometry
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 Alejandra Gaitán Purdue University 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.

Andrew Zimmer

Title: Complex analytic problems on domains with good intrinsic geometry

Abstract: In this talk, I will describe a new class of domains in complex Euclidean space which is defined in terms of the existence of a Kaehler metric with good geometric properties. This class is invariant under biholomorphism and includes many well-studied classes of domains such as strongly pseudoconvex domains, finite type domains in dimension two, convex domains, homogeneous domains, and embeddings of Teichmuller spaces. Further, certain analytic problems are tractable for domains in this family even when the boundary is non-smooth. In particular, it is possible to characterize the domains in this family where the dbar-Neumann operator on (0, q)-forms is compact (which generalizes an old result of Fu-Straube for convex domains).

Name

Title

Abstract

Name

Title

Abstract


Name

Title

Abstract

Name

Title

Abstract

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