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 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 11
+
|September 22
| Simon Marshall
+
|Alexei Poltoratski
| UW Madison
+
|UW Madison
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]
+
|[[#Alexei Poltoratski |   Dirac inner functions ]]
 
|  
 
|  
 
|-
 
|-
|'''Wednesday, Sept 12'''
+
|September 29
| Gunther Uhlmann 
+
|Polona Durcik
| University of Washington
+
| Chapman University
| Distinguished Lecture Series
+
|[[#linktoabstract |   Title ]]
| 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
+
|September 30
| Grad Student Seminar
+
|Joris Roos
|
+
|University of Massachusetts - Lowell
|
+
|[[#linktoabstract  |   Title ]]
|
 
|-
 
|Oct 9
 
| Hong Wang
 
| MIT
 
|[[#Hong Wang  |  About Falconer distance problem in the plane ]]
 
| Ruixiang
 
|-
 
|Oct 16
 
| Polona Durcik
 
| Caltech
 
|[[#Polona Durcik  |  Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]
 
| Joris  
 
|-
 
|Oct 23
 
| Song-Ying Li
 
| UC Irvine
 
|[[#Song-Ying Li  |  Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]
 
| Xianghong
 
|-
 
|Oct 30
 
|Grad student seminar
 
|
 
|
 
|
 
|-
 
|Nov 6
 
| Hanlong Fang
 
| UW Madison
 
|[[#Hanlong Fang  |  A generalization of the theorem of Weil and Kodaira on prescribing residues ]]
 
| Brian
 
|-
 
||'''Monday, Nov. 12, B139'''
 
| Kyle Hambrook
 
| San Jose State University
 
|[[#Kyle Hambrook  |  Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]
 
| Andreas
 
|-
 
|Nov 13
 
| Laurent Stolovitch
 
| Université de Nice - Sophia Antipolis
 
|[[#Laurent Stolovitch  |  Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]
 
|Xianghong
 
|-
 
|Nov 20
 
| Grad Student Seminar
 
|
 
|[[#linktoabstract  |   ]]
 
 
|  
 
|  
 
|-
 
|-
|Nov 27
+
|October 6
| No Seminar
+
|Andrew Zimmer
|  
+
|UW Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|Dec 4
+
|October 13
| No Seminar
+
|Hong Wang
|  
+
|Princeton/IAS
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|Jan 22
+
|October 20
| Brian Cook
+
|Kevin Luli
| Kent
+
|UC Davis
|[[#Brian Cook Equidistribution results for integral points on affine homogenous algebraic varieties ]]
+
|[[#linktoabstract Title ]]
| Street
 
|-
 
|Jan 29
 
| No Seminar
 
 
|  
 
|  
|[[#linktoabstract  |  Title ]]
 
|
 
 
|-
 
|-
|Feb 5, '''B239'''
+
|October 27
| Alexei Poltoratski
+
|Terence Harris
| Texas A&M
+
| Cornell University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Denisov
+
|  
 
|-
 
|-
|'''Friday, Feb 8'''
+
|Monday, November 2, 4 p.m.
| Aaron Naber
+
|Yuval Wigderson
| Northwestern University
+
|Stanford  University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| See colloquium website for location
 
|-
 
|Feb 12
 
| Shaoming Guo
 
| UW Madison
 
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets  ]]
 
 
|  
 
|  
 
|-
 
|-
|'''Wed, Feb 13, B239'''
+
|November 10
| Dean Baskin
+
|Óscar Domínguez
| TAMU
+
| Universidad Complutense de Madrid
|[[# Dean Baskin  |  Radiation fields for wave  equations ]]
 
|  Colloquium
 
|-
 
|'''Friday, Feb 15'''
 
| Lillian Pierce
 
| Duke
 
|[[# Lillian Pierce  |  Short character sums ]]
 
|  Colloquium
 
|-
 
|'''Monday,  Feb 18, 3:30 p.m, B239.'''
 
| Daniel Tataru
 
| UC Berkeley
 
|[[#lDaniel Tataru  |  A Morawetz inequality for water waves ]]
 
|  PDE Seminar
 
|-
 
|Feb 19
 
| Wenjia Jing (Tsinghua)
 
|Periodic  homogenization of Dirichlet problems in perforated domains: a unified proof
 
| PDE Seminar
 
|-
 
|Feb 26
 
| No Seminar
 
|
 
|
 
|-
 
|Mar 5
 
| Loredana Lanzani
 
| Syracuse University
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong
+
|  
 
|-
 
|-
|Mar 12
+
|November 17
| Trevor Leslie
+
|Tamas Titkos
| UW Madison
+
|BBS U of Applied Sciences and Renyi Institute
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
|
+
|  
 
|-
 
|-
|Mar 19
+
|November 24
|Spring Break!!!
+
|Shukun Wu
 +
|University of Illinois (Urbana-Champaign)
 +
||[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
 
|
 
 
|-
 
|-
|Mar 26
+
|December 1
| Person
+
| Jonathan Hickman
| Institution
+
| The University of Edinburgh
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|  
 
|-
 
|-
|Apr 2
+
|December 8
| Stefan Steinerberger
+
|TBA
| Yale
+
|  
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Shaoming, Andreas
+
|  
 
|-
 
|-
 
+
|February 2
|Apr 9
+
|Jongchon Kim
| Franc Forstnerič
+
| UBC
| Unversity of Ljubljana
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong, Andreas
+
|  
 
|-
 
|-
|Apr 16
+
|February 9
| Andrew Zimmer
+
|Bingyang Hu
| Louisiana State University
+
|Purdue University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong
+
|  
 
|-
 
|-
|Apr 23
+
|February 16
| Person
+
|David Beltran
| Institution
+
|UW - Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
 
|-
 
|Apr 30
 
| Person
 
| Institution
 
|[[#linktoabstract  |  Title ]]
 
| Sponsor
 
|-
 
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Simon Marshall===
+
===Alexei Poltoratski===
  
''Integrals of eigenfunctions on hyperbolic manifolds''
+
Title: Dirac inner functions
  
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.
+
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.
  
  
===Hong Wang===
+
===Name===
  
''About Falconer distance problem in the plane''
+
Title
  
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou.
+
Abstract
  
===Polona Durcik===
 
  
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''
+
===Name===
  
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.
+
Title
  
 +
Abstract
  
===Song-Ying Li===
 
  
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''
+
===Name===
  
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates
+
Title
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,
 
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the
 
Kohn Laplacian on strictly pseudoconvex hypersurfaces.
 
  
 +
Abstract
  
===Hanlong Fan===
 
  
''A generalization of the theorem of Weil and Kodaira on prescribing residues''
+
===Name===
  
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.
+
Title
  
===Kyle Hambrook===
+
Abstract
  
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''
+
=Extras=
 +
[[Blank Analysis Seminar Template]]
  
I will discuss my recent work on some problems concerning
 
Fourier decay and Fourier restriction for fractal measures on curves.
 
  
===Laurent Stolovitch===
+
Graduate Student Seminar:
  
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''
+
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
 
 
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$  are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.
 
 
 
 
 
===Brian Cook===
 
 
 
''Equidistribution results for integral points on affine homogenous algebraic varieties''
 
 
 
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.
 
 
 
===Shaoming Guo===
 
 
 
''Polynomial Roth theorems in Salem sets''
 
 
 
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik.
 
 
 
===Dean Baskin===
 
 
 
''Radiation fields for wave equations''
 
 
 
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.
 
 
 
===Lillian Pierce===
 
 
 
''Short character sums''
 
 
 
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.
 
 
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 

Latest revision as of 19:30, 19 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 Title
September 30 Joris Roos University of Massachusetts - Lowell Title
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.


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