Difference between revisions of "Analysis Seminar"

From UW-Math Wiki
Jump to: navigation, search
(Abstracts)
(Analysis Seminar Schedule)
 
(88 intermediate revisions by 8 users not shown)
Line 1: Line 1:
'''Analysis Seminar
+
'''Fall 2019 and Spring 2020 Analysis Seminar Series
 
'''
 
'''
  
Line 16: Line 16:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|Sept 11
+
|Sept 10
| Simon Marshall
+
| José Madrid
 +
| UCLA
 +
|[[#José Madrid  |  On the regularity of maximal operators on Sobolev Spaces ]]
 +
| Andreas, David
 +
|-
 +
|Sept 13 (Friday, B139)
 +
| Yakun Xi
 +
| University of  Rochester
 +
|[[#Yakun Xi  |  Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]
 +
| Shaoming
 +
|-
 +
|Sept 17
 +
| Joris Roos
 
| UW Madison
 
| UW Madison
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]
+
|[[#Joris Roos |   L^p improving estimates for maximal spherical averages ]]
|  
+
| Brian
 
|-
 
|-
|'''Wednesday, Sept 12'''
+
|Sept 20 (2:25 PM Friday, Room B139 VV)
| Gunther Uhlmann 
+
| Xiaojun Huang
| University of Washington
+
| Rutgers University–New Brunswick
| Distinguished Lecture Series
+
|[[#linktoabstract  |  A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]
| See colloquium website for location
+
| Xianghong
 
|-
 
|-
|'''Friday, Sept 14'''
+
|Sept 24
| Gunther Uhlmann 
+
| Person
| University of Washington
+
| Institution
| Distinguished Lecture Series
+
|[[#linktoabstract  |  Title ]]
| See colloquium website for location
+
| Sponsor
 
|-
 
|-
|Sept 18
+
|Oct 1
| Grad Student Seminar
+
| Xiaocheng Li
|  
+
| UW Madison
|
+
|[[#linktoabstract  |  Title ]]
|
+
| Simon
 
|-
 
|-
|Sept 25
+
|Oct 8
| Grad Student Seminar
+
| Jeff Galkowski
|
+
| Northeastern University
|
+
|[[#linktoabstract  |  Title ]]
|
+
| Betsy
 
|-
 
|-
|Oct 9
+
|Oct 15
| Hong Wang
+
| David Beltran
| MIT
+
| UW Madison
|[[#Hong Wang About Falconer distance problem in the plane ]]
+
|[[#linktoabstract Title ]]
| Ruixiang
+
| Brian
 
|-
 
|-
|Oct 16
+
|Oct 22
| Polona Durcik
+
| Laurent Stolovitch
| Caltech
+
| University of Nice Sophia-Antipolis
|[[#Polona Durcik Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]
+
|[[#linktoabstract Title ]]
| Joris
+
| Xianghong
 
|-
 
|-
|Oct 23
+
|<b>Wednesday Oct 23 in B129</b>
| Song-Ying Li
+
|Dominique Kemp
| UC Irvine
+
|Indiana University
|[[#Song-Ying Li  |   Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]
+
|tbd | tbd
| Xianghong
+
|Betsy
 
|-
 
|-
|Oct 30
+
|Oct 29
|Grad student seminar
+
| Bingyang Hu
|
 
|
 
|
 
|-
 
|Nov 6
 
| Hanlong Fang
 
 
| UW Madison
 
| UW Madison
|[[#Hanlong Fang A generalization of the theorem of Weil and Kodaira on prescribing residues ]]
+
|[[#linktoabstract Title ]]
| Brian
+
| Street
 
|-
 
|-
||'''Monday, Nov. 12, B139'''
+
|Nov 5
| Kyle Hambrook
+
| Kevin O'Neill
| San Jose State University
+
| UC Davis
|[[#Kyle Hambrook Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]
+
|[[#linktoabstract Title ]]
| Andreas
+
| Betsy
 
|-
 
|-
|Nov 13
+
|Nov 12
| Laurent Stolovitch
+
| Francesco di Plinio
| Université de Nice - Sophia Antipolis
+
| Washington University in St. Louis
|[[#Laurent Stolovitch Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]
+
|[[#linktoabstract Title ]]
|Xianghong
+
| Shaoming
 
|-
 
|-
|Nov 20
+
|Nov 19
| Grad Student Seminar
+
| Person
|  
+
| Institution
|[[#linktoabstract  |   ]]
+
|[[#linktoabstract  |   Title ]]
|  
+
| Sponsor
 
|-
 
|-
|Nov 27
+
|Nov 26
 
| No Seminar
 
| No Seminar
 
|  
 
|  
|[[#linktoabstract  |    ]]
+
|
 
|  
 
|  
 
|-
 
|-
|Dec 4
+
|Dec 3
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
| Sponsor
 +
|-
 +
|Dec 10
 
| No Seminar
 
| No Seminar
|[[#linktoabstract  |    ]]
 
 
|  
 
|  
 +
|
 +
|
 
|-
 
|-
|Jan 22
+
|Jan 21
| Brian Cook
 
| Kent
 
|[[#Brian Cook  |  Equidistribution results for integral points on affine homogenous algebraic varieties ]]
 
| Street
 
|-
 
|Jan 29
 
 
| No Seminar
 
| No Seminar
 
|  
 
|  
|[[#linktoabstract  |    ]]
+
|
 
|
 
|
 
|-
 
|-
|Feb 5, '''B239'''
+
|Jan 28
| Alexei Poltoratski
+
| Person
| Texas A&M
+
| Institution
|[[#Alexei Poltoratski Completeness of exponentials: Beurling-Malliavin and type problems ]]
+
|[[#linktoabstract Title ]]
| Denisov
+
| Sponsor
 
|-
 
|-
|'''Friday, Feb 8'''
+
|Feb 4
| Aaron Naber
+
| Person
| Northwestern University
+
| Institution
|[[#linktoabstract  |  A structure theory for spaces with lower Ricci curvature bounds ]]
+
|[[#linktoabstract  |  Title ]]
| See colloquium website for location
+
| Sponsor
 
|-
 
|-
|Feb 12
+
|Feb 11
| Shaoming Guo
+
| Person
| UW Madison
+
| Institution
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets   ]]
+
|[[#linktoabstract  Title ]]
|  
+
| Sponsor
 
|-
 
|-
|'''Wed, Feb 13, B239'''
+
|Feb 18
| Dean Baskin
+
| Person
| TAMU
+
| Institution
|[[# Dean Baskin Radiation fields for wave  equations ]]
+
|[[#linktoabstract Title ]]
| Colloquium
+
| Sponsor
 
|-
 
|-
|'''Friday, Feb 15'''
+
|Feb 25
| Lillian Pierce
+
| Person
| Duke
+
| Institution
|[[# Lillian Pierce Short character sums ]]
+
|[[#linktoabstract Title ]]
| Colloquium
+
| Sponsor
 
|-
 
|-
|'''Monday,  Feb 18, 3:30 p.m, B239.'''
+
|Mar 3
| Daniel Tataru
+
| Person
| UC Berkeley
+
| Institution
|[[#lDaniel Tataru A Morawetz inequality for water waves ]]
+
|[[#linktoabstract Title ]]
| PDE Seminar
+
| Sponsor
 
|-
 
|-
|Feb 19
+
|Mar 10
| Wenjia Jing
+
| Person
|Tsinghua University
+
| Institution
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof
+
|[[#linktoabstract |  Title ]]
| PDE Seminar
+
| Sponsor
 
|-
 
|-
|Feb 26
+
|Mar 17
| No Seminar
+
| Spring Break!
 
|
 
|
 
|
 
|
 +
|
 
|-
 
|-
|Mar 5
+
|Mar 24
| Loredana Lanzani
+
| Oscar Dominguez
| Syracuse University
+
| Universidad Complutense de Madrid
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong
+
| Andreas
 
|-
 
|-
|Mar 12
+
|Mar 31
| Trevor Leslie
 
| UW Madison
 
|[[#linktoabstract  |  Title ]]
 
|
 
|-
 
|Mar 19
 
|Spring Break!!!
 
|
 
|
 
|
 
|-
 
|Mar 26
 
 
| Person
 
| Person
 
| Institution
 
| Institution
Line 188: Line 184:
 
| Sponsor
 
| Sponsor
 
|-
 
|-
|Apr 2
+
|Apr 7
| Stefan Steinerberger
+
| Reserved
| Yale
+
| Institution
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Shaoming, Andreas
+
| Street
|-
 
 
 
|Apr 9
 
| Franc Forstnerič
 
| Unversity of Ljubljana
 
|[[#linktoabstract  |  Title ]]
 
| Xianghong, Andreas
 
 
|-
 
|-
|Apr 16
+
|Apr 14
| Andrew Zimmer
 
| Louisiana State University
 
|[[#linktoabstract  |  Title ]]
 
| Xianghong
 
|-
 
|Apr 23
 
 
| Person
 
| Person
 
| Institution
 
| Institution
Line 213: Line 196:
 
| Sponsor
 
| Sponsor
 
|-
 
|-
|Apr 30
+
|Apr 21
 
| Person
 
| Person
 
| Institution
 
| Institution
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
| Sponsor
 
| Sponsor
 +
|-
 +
|Apr 28
 +
| No Seminar
 +
|
 +
|
 +
|
 
|-
 
|-
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Simon Marshall===
+
===José Madrid===
 
 
''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.
 
 
 
 
 
===Hanlong Fan===
 
 
 
''A generalization of the theorem of Weil and Kodaira on prescribing residues''
 
  
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: On the regularity of maximal operators on Sobolev Spaces
  
===Kyle Hambrook===
+
Abstract:  In this talk, we will discuss the regularity properties (boundedness and
 +
continuity) of the classical and fractional maximal
 +
operators when these act on the Sobolev space W^{1,p}(\R^n). We will
 +
focus on the endpoint case p=1. We will talk about
 +
some recent results and current open problems.
  
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''
+
===Yakun Xi===
  
I will discuss my recent work on some problems concerning
+
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities
Fourier decay and Fourier restriction for fractal measures on curves.
 
  
===Laurent Stolovitch===
+
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.
  
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''
+
===Joris Roos===
  
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.
+
Title: L^p improving estimates for maximal spherical averages
  
 +
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.
 +
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.
 +
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.
  
===Brian Cook===
+
===Xiaojun Huang===
  
''Equidistribution results for integral points on affine homogenous algebraic varieties''
+
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries
  
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.
+
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.
  
===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.
 
  
 +
===Name===
  
===Alexei Poltoratski===
+
Title
  
''Completeness of exponentials: Beurling-Malliavin and type problems''
+
Abstract
  
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.
 
  
 +
===Name===
  
===Dean Baskin===
+
Title
  
''Radiation fields for wave equations''
+
Abstract
  
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===
+
===Name===
  
''Short character sums''
+
Title
  
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.
+
Abstract
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]

Latest revision as of 10:37, 17 September 2019

Fall 2019 and Spring 2020 Analysis Seminar Series

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 10 José Madrid UCLA On the regularity of maximal operators on Sobolev Spaces Andreas, David
Sept 13 (Friday, B139) Yakun Xi University of Rochester Distance sets on Riemannian surfaces and microlocal decoupling inequalities Shaoming
Sept 17 Joris Roos UW Madison L^p improving estimates for maximal spherical averages Brian
Sept 20 (2:25 PM Friday, Room B139 VV) Xiaojun Huang Rutgers University–New Brunswick A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries Xianghong
Sept 24 Person Institution Title Sponsor
Oct 1 Xiaocheng Li UW Madison Title Simon
Oct 8 Jeff Galkowski Northeastern University Title Betsy
Oct 15 David Beltran UW Madison Title Brian
Oct 22 Laurent Stolovitch University of Nice Sophia-Antipolis Title Xianghong
Wednesday Oct 23 in B129 Dominique Kemp Indiana University tbd Betsy
Oct 29 Bingyang Hu UW Madison Title Street
Nov 5 Kevin O'Neill UC Davis Title Betsy
Nov 12 Francesco di Plinio Washington University in St. Louis Title Shaoming
Nov 19 Person Institution Title Sponsor
Nov 26 No Seminar
Dec 3 Person Institution Title Sponsor
Dec 10 No Seminar
Jan 21 No Seminar
Jan 28 Person Institution Title Sponsor
Feb 4 Person Institution Title Sponsor
Feb 11 Person Institution Title Sponsor
Feb 18 Person Institution Title Sponsor
Feb 25 Person Institution Title Sponsor
Mar 3 Person Institution Title Sponsor
Mar 10 Person Institution Title Sponsor
Mar 17 Spring Break!
Mar 24 Oscar Dominguez Universidad Complutense de Madrid Title Andreas
Mar 31 Person Institution Title Sponsor
Apr 7 Reserved Institution Title Street
Apr 14 Person Institution Title Sponsor
Apr 21 Person Institution Title Sponsor
Apr 28 No Seminar

Abstracts

José Madrid

Title: On the regularity of maximal operators on Sobolev Spaces

Abstract: In this talk, we will discuss the regularity properties (boundedness and continuity) of the classical and fractional maximal operators when these act on the Sobolev space W^{1,p}(\R^n). We will focus on the endpoint case p=1. We will talk about some recent results and current open problems.

Yakun Xi

Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities

Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.

Joris Roos

Title: L^p improving estimates for maximal spherical averages

Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$. Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$. Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.

Xiaojun Huang

Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries

Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.



Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract

Extras

Blank Analysis Seminar Template