Difference between revisions of "Analysis Seminar"

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(2017-2018 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]]===
  
= 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 (Colloquium)
+
|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, 4:00 p.m.  in B131
+
|Oct 9
|Jonathan Hickman
+
| Hong Wang
|University of Chicago
+
| MIT
|[[#Jonathan Hickman | Factorising X^n  ]]
+
|[[#Hong Wang |   About Falconer distance problem in the plane ]]
|Andreas
+
| Ruixiang
 
|-
 
|-
|October 24
+
|Oct 16
| Xiaochun Li
+
| Polona Durcik
| UIUC
+
| Caltech
|[[#Xiaochun Li Recent progress on the pointwise convergence problems of Schroedinger equations ]]
+
|[[#Polona Durcik Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]
| Betsy
+
| Joris
 
|-
 
|-
|Thursday, October 26, 4:30 p.m. in B139
+
|Oct 23
| Fedor Nazarov
+
| Song-Ying Li
| Kent State University
+
| UC Irvine
|[[#Fedor Nazarov | The Lerner-Ombrosi-Perez bound in the Muckenhoupt Wheeden conjecture is sharp  ]]
+
|[[#Song-Ying Li |   Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]
| Sergey, Andreas
+
| Xianghong
 
|-
 
|-
|Friday, October 27, 4:00 p.m.  in B239
+
|Oct 30
| Stefanie Petermichl
+
|Grad student seminar
| University of Toulouse
+
|
|[[#Stefanie Petermichl  | Higher order Journé commutators  ]]
+
|
| Betsy, Andreas
+
|
 
|-
 
|-
|Wednesday, November 1, 4:00 p.m. in B239 (Colloquium)
+
|Nov 6
| Shaoming Guo
+
| Hanlong Fang
| Indiana University
+
|[[#Shaoming Guo  |  Parsell-Vinogradov systems in higher dimensions ]]
+
|  Andreas
+
|-
+
|November 14
+
| Naser Talebizadeh Sardari
+
 
| UW Madison
 
| UW Madison
|[[#Naser Talebizadeh Sardari Quadratic forms and the semiclassical eigenfunction hypothesis ]]
+
|[[#linktoabstract Title ]]
| Betsy
+
| Brian
 
|-
 
|-
|November 28
+
||'''Monday, Nov. 12'''
| Xianghong Chen
+
| Kyle Hambrook
| UW Milwaukee
+
| San Jose State University
|[[#Xianghong Chen  |  Some transfer operators on the circle with trigonometric weights ]]
+
| Betsy
+
|-
+
|Monday, December 4, 4:00, B139
+
|  Bartosz Langowski and Tomasz Szarek
+
| Institute of Mathematics, Polish Academy of Sciences
+
|[[#Bartosz Langowski and Tomasz Szarek  |  Discrete Harmonic Analysis in the Non-Commutative Setting ]]
+
| Betsy
+
|-
+
|December 12
+
| Alex Stokolos
+
| GA Southern
+
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
| Andreas
 
| Andreas
 
|-
 
|-
|Wednesday, December 13, 4:00, B239 (Colloquium)
+
|Nov 13
|Bobby Wilson
+
| Laurent Stolovitch
|MIT
+
| Université de Nice - Sophia Antipolis
|[[#Bobby Wilson | Projections in Banach Spaces and Harmonic Analysis ]]
+
|[[#Laurent Stolovitch  |   Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]
| Andreas
+
|Xianghong
 
|-
 
|-
|January 30
+
|Nov 20
 +
| No Seminar
 
|  
 
|  
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|February 6
+
|Nov 27
| 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
+
|Dec 4
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|February 20
+
|Jan 22
 +
| Brian Cook
 +
| Kent
 +
|[[#linktoabstract  |  Title ]]
 +
| Street
 +
|-
 +
|Jan 29
 +
| Trevor Leslie
 +
| UW Madison
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|February 27
+
|Feb 5
 +
| No seminar
 
|  
 
|  
|  
+
|
| [[#linkofabstract | Title]]
+
 
|
 
|
 
|-
 
|-
|Wednesday, March 7, 4:00 p.m.
+
|'''Friday, Feb 8'''
| Winfried Sickel
+
| Aaron Naber
|Friedrich-Schiller-Universität Jena
+
| Northwestern University
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|Andreas
+
| See colloquium website for location
 
|-
 
|-
|March 13
+
|Feb 12
|  
+
| No seminar
|
+
| [[#linkofabstract | Title]]
+
 
|
 
|
|-
 
|March 20
 
|
 
|
 
| [[#linkofabstract | Title]]
 
 
|
 
|
|-
 
|April 3
 
|
 
|
 
| [[#linkofabstract | Title]]
 
 
|
 
|
 
|-
 
|-
|April 10
+
|'''Friday, Feb 15'''
|  
+
| Charles Smart
|  
+
| University of Chicago
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| See colloquium website for information
 
|-
 
|-
|April 17
+
|Feb 19
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
|
+
| Sponsor
 
|-
 
|-
|April 24
+
|Feb 26
|  
+
| Person
|  
+
| Institution
| [[#linkofabstract | Title]]
+
|[[#linktoabstract  |   Title ]]
 +
| Sponsor
 +
|-
 +
|Mar 5
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Mar 12
 +
| No Seminar
 +
|
 +
|[[#linktoabstract  |  Title ]]
 
|
 
|
 
|-
 
|-
|May 1
+
|Mar 19
 +
|Spring Break!!!
 
|  
 
|  
|  
+
|
| [[#linkofabstract | Title]]
+
 
|
 
|
 
|-
 
|-
| May 16-18, Workshop in Fourier Analysis
+
|Apr 2
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| 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===
+
 
+
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
+
conjecture is sharp.
+
 
+
Abstract: We show that the upper bound $[w]_{A_1}\log (e+[w]_{A_1})$ for
+
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===
+
Title: Higher order Journé commutators
+
  
Abstract: We consider questions that stem from operator theory via Hankel and
+
''Integrals of eigenfunctions on hyperbolic manifolds''
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
+
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.
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 ===
+
===Hong Wang===
Title: Parsell-Vinogradov systems in higher dimensions
+
  
Abstract:
+
''About Falconer distance problem in the plane''
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===
+
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.
  
Title: Quadratic forms and the semiclassical eigenfunction hypothesis
+
===Polona Durcik===
  
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.
+
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''
  
===Xianghong Chen===
+
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:  Some transfer operators on the circle with trigonometric weights
 
  
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.
+
===Song-Ying Li===
  
===Bobby Wilson===
+
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''
  
Title: Projections in Banach Spaces and Harmonic Analysis
+
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates
 +
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: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.
 
  
===Dong Dong===
+
===Laurent Stolovitch===
  
Title: Hibert transforms in a 3 by 3 matrix and applications in number theory
+
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''
  
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.
+
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.
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]

Latest revision as of 15:28, 15 October 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 About Falconer distance problem in the plane Ruixiang
Oct 16 Polona Durcik Caltech Singular Brascamp-Lieb inequalities and extended boxes in R^n Joris
Oct 23 Song-Ying Li UC Irvine 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 Title Brian
Monday, Nov. 12 Kyle Hambrook San Jose State University Title Andreas
Nov 13 Laurent Stolovitch Université de Nice - Sophia Antipolis Equivalence of Cauchy-Riemann manifolds and multisummability theory Xianghong
Nov 20 No Seminar Title
Nov 27 Person Institution Title Sponsor
Dec 4 Person Institution Title Sponsor
Jan 22 Brian Cook Kent Title Street
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 No Seminar Title
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.


Hong Wang

About Falconer distance problem in the plane

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.

Polona Durcik

Singular Brascamp-Lieb inequalities and extended boxes in R^n

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.


Song-Ying Li

Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold

In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates 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.


Laurent Stolovitch

Equivalence of Cauchy-Riemann manifolds and multisummability theory

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.

Extras

Blank Analysis Seminar Template