Difference between revisions of "Analysis Seminar"

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(Summer/Fall 2017 Analysis Seminar Schedule)
(Analysis Seminar Schedule)
 
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The seminar will  meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
 
The seminar will  meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
  
If you wish to invite a speaker please  contact  Betsy at stovall(at)math
+
If you wish to invite a speaker please  contact  Brian at street(at)math
  
 
===[[Previous Analysis seminars]]===
 
===[[Previous Analysis seminars]]===
  
= Summer/Fall 2017 Analysis Seminar Schedule =
+
= Analysis Seminar Schedule =
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date   
 
!align="left" | date   
Line 16: Line 16:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 8 in B239
+
|Sept 11
| Tess Anderson
+
| Simon Marshall
| UW Madison
+
| Madison
|[[#linktoabstract |   A Spherical Maximal Function along the Primes]]
+
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]
|Tonghai
+
|  
 
|-
 
|-
|September 19
+
|'''Wednesday, Sept 12'''
| Brian Street
+
| Gunther Uhlmann 
| UW Madison
+
| University of Washington
|[[#Brian Street  |  Convenient Coordinates ]]
+
| Distinguished Lecture Series
| Betsy
+
| See colloquium website for location
 
|-
 
|-
|September 26
+
|'''Friday, Sept 14'''
| Hiroyoshi Mitake
+
| Gunther Uhlmann 
| Hiroshima University
+
| University of Washington
|[[#Hiroyoshi Mitake  |  Derivation of multi-layered interface system and its application ]]
+
| Distinguished Lecture Series
| Hung
+
| See colloquium website for location
 
|-
 
|-
|October 3
+
|Sept 18
| Joris Roos
+
| Grad Student Seminar
| UW Madison
+
|  
|[[#Joris Roos  |  A polynomial Roth theorem on the real line ]]
+
|
| Betsy
+
|
 
|-
 
|-
|October 10
+
|Sept 25
| Michael Greenblatt
+
| Grad Student Seminar
| UI Chicago
+
|
|[[#Michael Greenblatt  |  Maximal averages and Radon transforms for two-dimensional hypersurfaces ]]
+
|
| Andreas
+
|
 
|-
 
|-
|October 17
+
|Oct 2
| David Beltran
+
| Person
| Basque Center of Applied Mathematics
+
| Institution
|[[#David Beltran Fefferman-Stein inequalities ]]
+
|[[#linktoabstract Title ]]
| Andreas
+
| Sponsor
 
|-
 
|-
|Wednesday, October 18 in B131
+
|Oct 9
|Jonathan Hickman
+
| Hong Wang
|University of Chicago
+
| MIT
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
|Andreas
+
| Ruixiang
 
|-
 
|-
|October 24
+
|Oct 16
| Xiaochun Li
+
| Polona Durcik
| UIUC
+
| Caltech
|[[#Xiaochun Li Recent progress on the pointwise convergence problems of Schroedinger equations ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Joris
 
|-
 
|-
|Thursday, October 26
+
|Oct 23
| Fedya Nazarov
+
| Song-Ying Li
| Kent State University
+
| UC Irvine
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy, Andreas
+
| Xianghong
 
|-
 
|-
|Friday, October 27 in B239
+
|Oct 30
| Stefanie Petermichl
+
| Person
| University of Toulouse
+
| Institution
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy, Andreas
+
| Sponsor
 
|-
 
|-
|Wednesday, November 1 in B239
+
|Nov 6
| Shaoming Guo
+
| Hanlong Fang
| Indiana University
+
| UW Madison
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
| Brian
 
|-
 
|-
|November 14
+
||'''Monday, Nov. 12'''
| Naser Talebizadeh Sardari
+
| Kyle Hambrook
 +
| San Jose State University
 +
|[[#linktoabstract  |  Title ]]
 +
| Andreas
 +
|-
 +
|Nov 13
 +
| Laurent Stolovitch
 +
| Université de Nice - Sophia Antipolis
 +
|[[#linktoabstract  |  Title ]]
 +
|Xianghong
 +
|-
 +
|Dec 4
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Jan 22
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Jan 29
 +
| Trevor Leslie
 
| UW Madison
 
| UW Madison
|[[#linktoabstract  |  Quadratic forms and the semiclassical eigenfunction hypothesis ]]
+
|[[#linktoabstract  |  Title ]]
| Betsy
+
|  
 +
|-
 +
|Feb 5
 +
| No seminar
 +
|
 +
|
 +
|
 
|-
 
|-
|November 28
+
|'''Friday, Feb 8'''
| Xianghong Chen
+
| Aaron Naber
| UW Milwaukee
+
| Northwestern University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Betsy
+
| See colloquium website for location
 
|-
 
|-
|December 5
+
|Feb 12
| Tentatively reserved (betsy, 10/1)
+
| No seminar
 
|
 
|
 +
|
 +
|
 +
|-
 +
|'''Friday, Feb 15'''
 +
| Charles Smart
 +
| University of Chicago
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 +
| See colloquium website for information
 +
|-
 +
|Feb 19
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Feb 26
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Mar 5
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Mar 12
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Mar 19
 +
|Spring Break!!!
 +
|
 +
|
 
|
 
|
 
|-
 
|-
|December 12
+
|Apr 2
| Alex Stokolos
+
| Person
| GA Southern
+
| Institution
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
| Sponsor
 +
|-
 +
|Apr 9
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Apr 9
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Apr 16
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Apr 23
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Apr 30
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 
|-
 
|-
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Brian Street===
+
===Simon Marshall===
 
+
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===
+
''Integrals of eigenfunctions on hyperbolic manifolds''
  
Title: Derivation of multi-layered interface system and its application
+
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:  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===
+
===Name===
  
Title: A polynomial Roth theorem on the real line
+
Title
  
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.
+
Abstract
  
===Michael Greenblatt===
 
  
Title:  Maximal averages and Radon transforms for two-dimensional hypersurfaces
+
===Name===
  
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.
+
Title
  
===David Beltran===
+
Abstract
  
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.
+
===Name===
  
===Xiaochun Li ===
+
Title
  
Title:  Recent progress on the pointwsie convergence problems of Schrodinger equations
+
Abstract
  
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.
 
  
===Naser Talebizadeh Sardari===
+
===Name===
  
Title: Quadratic forms and the semiclassical eigenfunction hypothesis
+
Title
  
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.
+
Abstract
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]

Latest revision as of 09:52, 11 September 2018

Analysis Seminar

The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.

If you wish to invite a speaker please contact Brian at street(at)math

Previous Analysis seminars

Analysis Seminar Schedule

date speaker institution title host(s)
Sept 11 Simon Marshall Madison Integrals of eigenfunctions on hyperbolic manifolds
Wednesday, Sept 12 Gunther Uhlmann University of Washington Distinguished Lecture Series 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 Grad Student Seminar
Oct 2 Person Institution Title Sponsor
Oct 9 Hong Wang MIT Title Ruixiang
Oct 16 Polona Durcik Caltech Title Joris
Oct 23 Song-Ying Li UC Irvine Title Xianghong
Oct 30 Person Institution Title Sponsor
Nov 6 Hanlong Fang UW Madison Title Brian
Monday, Nov. 12 Kyle Hambrook San Jose State University Title Andreas
Nov 13 Laurent Stolovitch Université de Nice - Sophia Antipolis Title Xianghong
Dec 4 Person Institution Title Sponsor
Jan 22 Person Institution Title Sponsor
Jan 29 Trevor Leslie UW Madison Title
Feb 5 No seminar
Friday, Feb 8 Aaron Naber Northwestern University Title See colloquium website for location
Feb 12 No seminar
Friday, Feb 15 Charles Smart University of Chicago Title See colloquium website for information
Feb 19 Person Institution Title Sponsor
Feb 26 Person Institution Title Sponsor
Mar 5 Person Institution Title Sponsor
Mar 12 Person Institution Title Sponsor
Mar 19 Spring Break!!!
Apr 2 Person Institution Title Sponsor
Apr 9 Person Institution Title Sponsor
Apr 9 Person Institution Title Sponsor
Apr 16 Person Institution Title Sponsor
Apr 23 Person Institution Title Sponsor
Apr 30 Person Institution Title Sponsor

Abstracts

Simon Marshall

Integrals of eigenfunctions on hyperbolic manifolds

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.


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract

Extras

Blank Analysis Seminar Template