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.
  
If you wish to invite a speaker please contact Betsy at stovall(at)math
+
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]]===
 
  
= 2017-2018 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 19:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 8 in B239
+
|September 22
| Tess Anderson
+
|Alexei Poltoratski
| UW Madison
+
|UW Madison
|[[#linktoabstract  |  A Spherical Maximal Function along the Primes]]
+
|[[#linktoabstract  |  Title ]]
|Tonghai
+
|  
|-
 
|September 19
 
| Brian Street
 
| UW Madison
 
|[[#Brian Street  |  Convenient Coordinates ]]
 
| Betsy
 
|-
 
|September 26
 
| Hiroyoshi Mitake
 
| Hiroshima University
 
|[[#Hiroyoshi Mitake  |  Derivation of multi-layered interface system and its application ]]
 
| Hung
 
|-
 
|October 3
 
| Joris Roos
 
| UW Madison
 
|[[#Joris Roos  |  A polynomial Roth theorem on the real line ]]
 
| Betsy
 
|-
 
|October 10
 
| Michael Greenblatt
 
| UI Chicago
 
|[[#Michael Greenblatt  |  Maximal averages and Radon transforms for two-dimensional hypersurfaces ]]
 
| Andreas
 
|-
 
|October 17
 
| David Beltran
 
| Basque Center of Applied Mathematics
 
|[[#David Beltran  |  Fefferman-Stein inequalities ]]
 
| Andreas
 
|-
 
|Wednesday, October 18, 4:00 p.m.  in B131
 
|Jonathan Hickman
 
|University of Chicago
 
|[[#Jonathan Hickman  |  Factorising X^n  ]]
 
|Andreas
 
|-
 
|October 24
 
| Xiaochun Li
 
| UIUC
 
|[[#Xiaochun Li  |  Recent progress on the pointwise convergence problems of Schroedinger equations ]]
 
| Betsy
 
|-
 
|Thursday, October 26, 4:30 p.m. in B139
 
| Fedor Nazarov
 
| Kent State University
 
|[[#Fedor Nazarov  |  The Lerner-Ombrosi-Perez bound in the Muckenhoupt Wheeden conjecture is sharp  ]]
 
| Sergey, Andreas
 
|-
 
|Friday, October 27, 4:00 p.m.  in B239
 
| Stefanie Petermichl
 
| University of Toulouse
 
|[[#Stefanie Petermichl  | Higher order Journé commutators  ]]
 
| Betsy, Andreas
 
|-
 
|Wednesday, November 1, 4:00 p.m. in B239
 
| Shaoming Guo
 
| Indiana University
 
|[[#Shaoming Guo  |  Parsell-Vinogradov systems in higher dimensions ]]
 
|  Andreas
 
|-
 
|November 14
 
| Naser Talebizadeh Sardari
 
| UW Madison
 
|[[#Naser Talebizadeh Sardari  |  Quadratic forms and the semiclassical eigenfunction hypothesis ]]
 
| Betsy
 
 
|-
 
|-
|November 28
+
|September 29
| Xianghong Chen
+
|Polona Durcik
| UW Milwaukee
+
| Chapman University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|  
 
|-
 
|-
|December 5
+
|September 30
| Bartosz Langowski and Tomasz Szarek
+
|Joris Roos
| Institute of Mathematics, Polish Academy of Sciences
+
|University of Massachusetts - Lowell
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
|  
 
|-
 
|-
|December 12
+
|October 6
| Alex Stokolos
+
|Andrew Zimmer
| GA Southern
+
|UW Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
 
|-
 
|-
 
|January 30
 
|
 
 
|  
 
|  
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|February 6
+
|October 13
| Dong Dong
+
|Hong Wang
| UIUC
+
|Princeton/IAS
| [[#Dong Dong | Hibert transforms in a 3 by 3 matrix and applications in number theory]]
+
|[[#linktoabstract  |   Title ]]
|Betsy
 
|-
 
|February 13
 
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|February 20
+
|October 20
 +
|Kevin Luli
 +
|UC Davis
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|February 27
+
|October 27
|  
+
|Terence Harris
 +
| Cornell University
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|March 6
+
|November 3
|  
+
|No seminar
 
|  
 
|  
| [[#linkofabstract | Title]]
 
 
|
 
|
|-
 
|March 13
 
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|March 20
+
|November 10
 +
|Óscar Domínguez
 +
| Universidad Complutense de Madrid
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|April 3
+
|November 17
|  
+
|Tamas Titkos
 +
|BBS U of Applied Sciences and Renyi Institute
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|April 10
+
|November 24
 +
| No seminar
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
 
|
 
|
|-
 
|April 17
 
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|April 24
+
|December 1
|  
+
| Jonathan Hickman
 +
| The University of Edinburgh
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|May 1
+
|December 8
 +
|David Beltran
 +
| UW Madison
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
 +
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Brian Street===
+
===Name===
 
 
Title:  Convenient Coordinates
 
 
 
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".
 
 
 
===Hiroyoshi Mitake===
 
 
 
Title:  Derivation of multi-layered interface system and its application
 
 
 
Abstract:  In this talk, I will propose a multi-layered interface system which can
 
be formally derived by the singular limit of the weakly coupled system of
 
the Allen-Cahn equation.  By using the level set approach, this system can be
 
written as a quasi-monotone degenerate parabolic system.
 
We give results of the well-posedness of viscosity solutions, and study the
 
singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.
 
 
 
===Joris Roos===
 
 
 
Title: A polynomial Roth theorem on the real line
 
 
 
Abstract: For a polynomial P of degree greater than one, we show the existence of patterns of the form (x,x+t,x+P(t)) with a gap estimate on t in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our proof is a combination of Bourgain’s approach and more recent methods that were originally developed for the study of the bilinear Hilbert transform along curves. This talk is based on a joint work with Polona Durcik and Shaoming Guo.
 
 
 
===Michael Greenblatt===
 
 
 
Title:  Maximal averages and Radon transforms for two-dimensional hypersurfaces
 
 
 
Abstract:  A general local result concerning L^p boundedness of maximal averages over 2D hypersurfaces is described, where p > 2. The surfaces are allowed to have either the traditional smooth density function or a singularity growing as |(x,y)|^{-t} for some 0 < t < 2. This result is a generalization of a theorem of Ikromov, Kempe, and Mueller. Similar methods can be used to show sharp L^p to L^p_a Sobolev estimates for associated Radon transform operators when p is in a certain interval containing 2.
 
 
 
===David Beltran===
 
 
 
Title:  Fefferman Stein Inequalities
 
 
 
Abstract:  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.
 
  
===Jonathan Hickman===
+
Title
  
Title: Factorising X^n.
+
Abstract
  
Question: how many ways can the polynomial $X^n$ be factorised as a product of linear factors? Answer: it depends on the ring... In this talk I will describe joint work with Jim Wright investigating certain exponential sum estimates over rings of integers modulo N. This theory serves as a discrete analogue of the (euclidean) Fourier restriction problem, a central question in contemporary harmonic analysis. In particular, as part of this study, the question of counting the number of factorisations of polynomials over such rings naturally arises. I will describe how these number-theoretic considerations can themselves be approached via methods from harmonic analysis.
 
  
===Xiaochun Li ===
+
===Name===
  
Title:  Recent progress on the pointwise convergence problems of Schrodinger equations
+
Title
  
Abstract:  Recently, Guth, Du and I solved the pointwise convergence problem of Schrodinger equations in two-dimensional case. We proved that the solution to free Schrodinger equation in R^2 converges to its initial data, provided the initial data belongs to H^s for s larger than 1/3.  This result is sharp, up to the end point, due to Bourgain's example. The proof relies on the polynomial partitioning method and  the decoupling method. In addition, the pointwise convergence problem is closely related to Fourier restriction conjecture.
+
Abstract
  
===Fedor Nazarov=== 
 
  
Title: The Lerner-Ombrosi-Perez bound in the Muckenhoupt-Wheeden
+
===Name===
conjecture is sharp.
 
  
Abstract: We show that the upper bound $[w]_{A_1}\log (e+[w]_{A_1})$ for
+
Title
the norm of the Hilbert transform on the line as an operator from $L^1(w)$
 
to $L^{1,\infty}(w)$ cannot be improved in general. This is a joint work
 
with Andrei Lerner and Sheldy Ombrosi.
 
  
 +
Abstract
  
===Stefanie Petermichl===
 
Title: Higher order Journé commutators
 
  
Abstract: We consider questions that stem from operator theory via Hankel and
+
===Name===
Toeplitz forms and target (weak) factorisation of Hardy spaces. In
 
more basic terms, let us consider a function on the unit circle in its
 
Fourier representation. Let P_+ denote the projection onto
 
non-negative and P_- onto negative frequencies. Let b denote
 
multiplication by the symbol function b. It is a classical theorem by
 
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and
 
only if b is in an appropriate space of functions of bounded mean
 
oscillation. The necessity makes use of a classical factorisation
 
theorem of complex function theory on the disk. This type of question
 
can be reformulated in terms of commutators [b,H]=bH-Hb with the
 
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such
 
as in the real variable setting, in the multi-parameter setting or
 
other, these classifications can be very difficult.
 
  
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and
+
Title
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of
 
spaces of bounded mean oscillation via L^p boundedness of commutators.
 
We present here an endpoint to this theory, bringing all such
 
characterisation results under one roof.
 
  
The tools used go deep into modern advances in dyadic harmonic
+
Abstract
analysis, while preserving the Ansatz from classical operator theory.
 
  
===Shaoming Guo ===
 
Title: Parsell-Vinogradov systems in higher dimensions
 
  
Abstract:
+
===Name===
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.
 
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.
 
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.
 
  
===Naser Talebizadeh Sardari===
+
Title
  
Title: Quadratic forms and the semiclassical eigenfunction hypothesis
+
Abstract
  
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.
 
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]

Latest revision as of 17:35, 12 August 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.

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 Title
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
November 3 No seminar
November 10 Óscar Domínguez Universidad Complutense de Madrid Title
November 17 Tamas Titkos BBS U of Applied Sciences and Renyi Institute Title
November 24 No seminar
December 1 Jonathan Hickman The University of Edinburgh Title
December 8 David Beltran UW Madison Title

Abstracts

Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract


Extras

Blank Analysis Seminar Template