Difference between revisions of "Analysis Seminar"

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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]]===
  
= 2017-2018 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
+
|Sept 18
| Brian Street
+
| Person
| UW Madison
+
| Institution
|[[#Brian Street Convenient Coordinates ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Sponsor
 
|-
 
|-
|September 26
+
|Sept 25
| Hiroyoshi Mitake
+
| Gunther Uhlman
| Hiroshima University
+
| University of Washington
|[[#Hiroyoshi Mitake Derivation of multi-layered interface system and its application ]]
+
|[[#linktoabstract Title ]]
| Hung
+
| Qin Li
 
|-
 
|-
|October 3
+
|Oct 2
| Joris Roos
+
| Person
| UW Madison
+
| Institution
|[[#Joris Roos A polynomial Roth theorem on the real line ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Sponsor
 
|-
 
|-
|October 10
+
|Oct 9
| Michael Greenblatt
+
| Person
| UI Chicago
+
| Institution
|[[#Michael Greenblatt Maximal averages and Radon transforms for two-dimensional hypersurfaces ]]
+
|[[#linktoabstract Title ]]
| Andreas
+
| Sponsor
 
|-
 
|-
|October 17
+
|Oct 16
| David Beltran
+
| Person
| Basque Center of Applied Mathematics
+
| Institution
|[[#David Beltran Fefferman-Stein inequalities ]]
+
|[[#linktoabstract Title ]]
| Andreas
+
| Sponsor
 
|-
 
|-
|Wednesday, October 18, 4:00 p.m.  in B131
+
|Oct 23
|Jonathan Hickman
+
| Person
|University of Chicago
+
| Institution
|[[#Jonathan Hickman | Factorising X^n  ]]
+
|[[#linktoabstract |   Title ]]
|Andreas
+
| Sponsor
 
|-
 
|-
|October 24
+
|Oct 30
| Xiaochun Li
+
| Person
| UIUC
+
| Institution
|[[#Xiaochun Li Recent progress on the pointwise convergence problems of Schroedinger equations ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Sponsor
 
|-
 
|-
|Thursday, October 26, 4:30 p.m. in B139
+
|Nov 6
| Fedor Nazarov
+
| Person
| Kent State University
+
| Institution
|[[#Fedor Nazarov | The Lerner-Ombrosi-Perez bound in the Muckenhoupt Wheeden conjecture is sharp  ]]
+
|[[#linktoabstract |   Title ]]
| Sergey, Andreas
+
| Sponsor
 
|-
 
|-
|Friday, October 27, 4:00 p.m.  in B239
+
|Nov 13
| Stefanie Petermichl
+
| Person
| University of Toulouse
+
| Institution
|[[#Stefanie Petermichl | Higher order Journé commutators   ]]
+
|[[#linktoabstract Title ]]
| Betsy, Andreas
+
| Sponsor
 
|-
 
|-
|Wednesday, November 1, 4:00 p.m. in B239 (Colloquium)
+
|Nov 20
| Shaoming Guo
+
| Thanksgiving!
| Indiana University
+
|  
|[[#Shaoming Guo  |  Parsell-Vinogradov systems in higher dimensions ]]
+
|
| Andreas
+
|
 
|-
 
|-
|November 14
+
|Dec 4
| Naser Talebizadeh Sardari
+
| Person
| UW Madison
+
| Institution
|[[#Naser Talebizadeh Sardari Quadratic forms and the semiclassical eigenfunction hypothesis ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Sponsor
 
|-
 
|-
|November 28
+
|Jan 22
| Xianghong Chen
+
| Person
| UW Milwaukee
+
| Institution
|[[#Xianghong Chen Some transfer operators on the circle with trigonometric weights ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Sponsor
 
|-
 
|-
|Monday, December 4, 4:00, B139
+
|Jan 29
| Bartosz Langowski and Tomasz Szarek
+
| Person
| Institute of Mathematics, Polish Academy of Sciences
+
| Institution
|[[#Bartosz Langowski and Tomasz Szarek Discrete Harmonic Analysis in the Non-Commutative Setting ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Sponsor
 
|-
 
|-
|December 12
+
|Feb 5
| Alex Stokolos
+
| Person
| GA Southern
+
| Institution
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Andreas
+
| Sponsor
 
|-
 
|-
|Wednesday, December 13, 4:00, B239 (Colloquium)
+
|Feb 12
|Bobby Wilson
+
| Person
|MIT
+
| Institution
|[[#Bobby Wilson | Projections in Banach Spaces and Harmonic Analysis ]]
+
|[[#linktoabstract  |   Title ]]
| Andreas
+
| Sponsor
 
|-
 
|-
|January 30
+
|Feb 19
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|February 6
+
|Feb 26
| Dong Dong
+
| Person
| UIUC
+
| Institution
| [[#Dong Dong | Hibert transforms in a 3 by 3 matrix and applications in number theory]]
+
|[[#linktoabstract  |   Title ]]
|Betsy
+
| Sponsor
 
|-
 
|-
|February 13
+
|Mar 5
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|February 20
+
|Mar 12
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|February 27
+
|Mar 19
 +
|Spring Break!!!
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
 
|
 
|
|-
 
|Wednesday, March 7, 4:00 p.m.
 
| Winfried Sickel
 
|Friedrich-Schiller-Universität Jena
 
| [[#linkofabstract | Title]]
 
|Andreas
 
|-
 
|March 13
 
|
 
|
 
| [[#linkofabstract | Title]]
 
 
|
 
|
 
|-
 
|-
|March 20
+
|Apr 2
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|April 3
+
|Apr 9
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|April 10
+
|Apr 9
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|April 17
+
|Apr 16
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|April 24
+
|Apr 23
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|May 1
+
|Apr 30
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#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===
+
 
+
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: Factorising X^n.
+
 
+
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 ===
+
 
+
Title:  Recent progress on the pointwise convergence problems of Schrodinger equations
+
 
+
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.
+
 
+
===Fedor Nazarov=== 
+
  
Title: The Lerner-Ombrosi-Perez bound in the Muckenhoupt-Wheeden
+
''Integrals of eigenfunctions on hyperbolic manifolds''
conjecture is sharp.
+
  
Abstract: We show that the upper bound $[w]_{A_1}\log (e+[w]_{A_1})$ for
+
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.
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.
+
  
  
===Stefanie Petermichl===
+
===Name===
Title: Higher order Journé commutators
+
  
Abstract: We consider questions that stem from operator theory via Hankel and
+
Title
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
+
Abstract
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
 
analysis, while preserving the Ansatz from classical operator theory.
 
  
===Shaoming Guo ===
+
===Name===
Title: Parsell-Vinogradov systems in higher dimensions
+
  
Abstract:
+
Title
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===
+
Abstract
  
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===
  
===Xianghong Chen===
+
Title
  
Title:  Some transfer operators on the circle with trigonometric weights
+
Abstract
  
Abstract:  A transfer operator is an averaging operator over the preimages of a given map. Certain dynamical properties of the map can be studied through its associated transfer operator. In this talk we will introduce a class of weighted transfer operators associated to the Bernoulli maps on the circle (i.e. multiplication by a given integer, mod 1). We will illustrate how the spectral properties of these operators may depend on the specific weight chosen and demonstrate multiple phase transitions. We also present some results on evaluating the spectral radii and corresponding eigenfunctions of these operators, as well as their connections to Fourier analysis. This is joint work with Hans Volkmer.
 
  
===Dong Dong===
+
===Name===
  
Title: Hibert transforms in a 3 by 3 matrix and applications in number theory
+
Title
  
Abstract:  This talk could interest both analysts and number theorists. I will first present 35 variants of Hilbert transforms, with a focus on their connections with ergodic theory, number theory, and combinatorics. Then I will show how to use Fourier analysis tools to reduce a number theory problem (Roth theorem) to an algebraic geometry problem: this joint work Li and Sawin fully answers a question of Bourgain and Chang about three-term polynomial progressions in subsets of finite fields. I guarantee that a second-year graduate student can understand at least 50% of the talk.
+
Abstract
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]

Latest revision as of 16:48, 9 July 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
Sept 18 Person Institution Title Sponsor
Sept 25 Gunther Uhlman University of Washington Title Qin Li
Oct 2 Person Institution Title Sponsor
Oct 9 Person Institution Title Sponsor
Oct 16 Person Institution Title Sponsor
Oct 23 Person Institution Title Sponsor
Oct 30 Person Institution Title Sponsor
Nov 6 Person Institution Title Sponsor
Nov 13 Person Institution Title Sponsor
Nov 20 Thanksgiving!
Dec 4 Person Institution Title Sponsor
Jan 22 Person Institution Title Sponsor
Jan 29 Person Institution Title Sponsor
Feb 5 Person Institution Title Sponsor
Feb 12 Person Institution Title Sponsor
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