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.
 +
The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier, or on different days, to accomodate speakers).
  
If you wish to invite a speaker please contact Brian at street(at)math
+
Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230
  
===[[Previous Analysis seminars]]===
+
If you'd like to suggest  speakers for the spring semester please contact David and Andreas (dbeltran at math, seeger at math).
  
= 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 22:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|Sept 11
+
|September 22
| Simon Marshall
+
|Alexei Poltoratski
| UW Madison
+
|UW Madison
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]
+
|[[#Alexei Poltoratski |   Dirac inner functions ]]
 
|  
 
|  
 
|-
 
|-
|'''Wednesday, Sept 12'''
+
|September 29
| Gunther Uhlmann 
+
|Joris Roos
| University of Washington
+
|University of Massachusetts - Lowell
| Distinguished Lecture Series
+
|[[#Polona Durcik and Joris Rooslinktoabstract  |  A triangular Hilbert transform with curvature, I ]]
| See colloquium website for location
+
|  
 
|-
 
|-
|'''Friday, Sept 14'''
+
|Wednesday September 30, 4 p.m.
| Gunther Uhlmann 
+
|Polona Durcik
| University of Washington
+
|Chapman University
| Distinguished Lecture Series
+
|[[#Polona Durcik and Joris Roos  |  A triangular Hilbert transform with curvature, II ]]
| See colloquium website for location
+
|  
 
|-
 
|-
|Sept 18
+
|October 6
| Grad Student Seminar
+
|Andrew Zimmer
 +
|UW Madison
 +
|[[#Andrew Zimmer  |  Complex analytic problems on domains with good intrinsic geometry ]]
 
|  
 
|  
|
 
|
 
 
|-
 
|-
|Sept 25
+
|October 13
| Grad Student Seminar
+
|Hong Wang
|
+
|Princeton/IAS
|
+
|[[#Hong Wang  |  Improved decoupling for the parabola ]]
|
+
|  
 
|-
 
|-
|Oct 9
+
|October 20
| Hong Wang
+
|Kevin Luli
| MIT
+
|UC Davis
|[[#Hong Wang About Falconer distance problem in the plane ]]
+
|[[#Kevin Luli Smooth Nonnegative Interpolation ]]
| Ruixiang
+
|  
 
|-
 
|-
|Oct 16
+
|October 21, 4.00 p.m.
| Polona Durcik
+
|Niclas Technau
| Caltech
+
|UW Madison
|[[#Polona Durcik Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]
+
|[[#Niclas Technau Number theoretic applications of oscillatory integrals ]]
| Joris
+
|  
 
|-
 
|-
|Oct 23
+
|October 27
| Song-Ying Li
+
|Terence Harris
| UC Irvine
+
| Cornell University
|[[#Song-Ying Li Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]
+
|[[#Terence Harris Low dimensional pinned distance sets via spherical averages ]]
| Xianghong
+
|  
 
|-
 
|-
|Oct 30
+
|Monday, November 2, 4 p.m.
|Grad student seminar
+
|Yuval Wigderson
|
+
|Stanford  University
|
+
|[[#linktoabstract  |  Title ]]
|
+
|  
 
|-
 
|-
|Nov 6
+
|November 10
| Hanlong Fang
+
|Óscar Domínguez
| UW Madison
+
| Universidad Complutense de Madrid
|[[#Hanlong Fang A generalization of the theorem of Weil and Kodaira on prescribing residues ]]
+
|[[#linktoabstract Title ]]
| Brian
+
|  
 
|-
 
|-
||'''Monday, Nov. 12, B139'''
+
|November 17
| Kyle Hambrook
+
|Tamas Titkos
| San Jose State University
+
|BBS U of Applied Sciences and Renyi Institute
|[[#Kyle Hambrook Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]
+
|[[#linktoabstract Title ]]
| Andreas
+
|  
 
|-
 
|-
|Nov 13
+
|November 24
| Laurent Stolovitch
+
|Shukun Wu
| Université de Nice - Sophia Antipolis
+
|University of Illinois (Urbana-Champaign)
|[[#Laurent Stolovitch Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]
+
||[[#linktoabstract Title ]]  
|Xianghong
+
|  
 
|-
 
|-
|Nov 20
+
|December 1
| Grad Student Seminar
+
| Jonathan Hickman
 +
| The University of Edinburgh
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|[[#linktoabstract  |   ]]
+
|-
 +
|December 8
 +
|Alejandra Gaitán
 +
| Purdue University
 +
|[[#linktoabstract  |   Title ]]
 
|  
 
|  
 
|-
 
|-
|Nov 27
+
|February 2
| No Seminar
+
|Jongchon Kim
|  
+
| UBC
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|Dec 4
+
|February 9
| No Seminar
+
|Bingyang Hu
|  
+
|Purdue University
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
 
|-
 
|-
|Jan 22
+
|February 16
| Brian Cook
+
|Krystal Taylor
| Kent
+
|The Ohio State University
|[[#Brian Cook Equidistribution results for integral points on affine homogenous algebraic varieties ]]
+
|[[#linktoabstract Title ]]
| Street
+
|
 
|-
 
|-
|Jan 29
+
|February 23
| No Seminar
+
|Dominique Maldague
|  
+
|MIT
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|
 
|
 
|-
 
|-
|Feb 5, '''B239'''
+
|March 2
| Alexei Poltoratski
+
|Diogo Oliveira e Silva
| Texas A&M
+
|University of Birmingham
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Denisov
+
|
 
|-
 
|-
|'''Friday, Feb 8'''
+
|March 9
| Aaron Naber
+
|
| Northwestern University
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| See colloquium website for location
+
|
|-
 
|Feb 12
 
| Shaoming Guo
 
| UW Madison
 
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets  ]]
 
|  
 
 
|-
 
|-
|'''Wed, Feb 13, B239'''
+
|March 16
| Dean Baskin
+
|Ziming Shi
| TAMU
+
|Rutgers University
|[[# Dean Baskin  |  Radiation fields for wave  equations ]]
 
|  Colloquium
 
|-
 
|'''Friday, Feb 15'''
 
| Lillian Pierce
 
| Duke
 
|[[# Lillian Pierce  |  Short character sums ]]
 
|  Colloquium
 
|-
 
|'''Monday,  Feb 18, 3:30 p.m, B239.'''
 
| Daniel Tataru
 
| UC Berkeley
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
|
+
|
 
|-
 
|-
|Feb 19
+
|March 23
| PDE seminar in B139
 
 
|
 
|
 
|
 
|
 +
|[[#linktoabstract  |  Title ]]
 
|
 
|
 
|-
 
|-
|Feb 26
+
|March 30
| No Seminar
 
 
|
 
|
 
|
 
|
|-
 
|Mar 5
 
| Loredana Lanzani
 
| Syracuse University
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong
+
|
 
|-
 
|-
|Mar 12
+
|April 6
| Trevor Leslie
+
|
| UW Madison
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
 
|
 
|
 
|-
 
|-
|Mar 19
+
|April 13
|Spring Break!!!
 
|
 
 
|
 
|
 
|
 
|
|-
 
|Mar 26
 
| Person
 
| Institution
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Sponsor
+
|
 
|-
 
|-
|Apr 2
+
|April 20
| Stefan Steinerberger
+
|
| Yale
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Shaoming, Andreas
+
|
 
|-
 
|-
 
+
|April 27
|Apr 9
+
|
| Franc Forstnerič
+
|
| Unversity of Ljubljana
 
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong, Andreas
+
|
 
|-
 
|-
|Apr 16
+
|May 4
| Andrew Zimmer
+
|
| Louisiana State University
+
|
 
|[[#linktoabstract  |  Title ]]
 
|[[#linktoabstract  |  Title ]]
| Xianghong
 
|-
 
|Apr 23
 
| Person
 
| Institution
 
|[[#linktoabstract  |  Title ]]
 
| Sponsor
 
|-
 
|Apr 30
 
| Person
 
| Institution
 
|[[#linktoabstract  |  Title ]]
 
| Sponsor
 
|-
 
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Simon Marshall===
+
===Alexei Poltoratski===
 
 
''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.
+
Title: Dirac inner functions
  
 +
Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations.
 +
We will discuss connections between problems in complex function theory, spectral and scattering problems for differential
 +
operators and the non-linear Fourier transform.
  
===Hong Wang===
+
===Polona Durcik and Joris Roos===
  
''About Falconer distance problem in the plane''
+
Title: A triangular Hilbert transform with curvature, I & II.
  
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.  
+
Abstract: The triangular Hilbert is a two-dimensional bilinear singular
 +
originating in time-frequency analysis. No Lp bounds are currently
 +
known for this operator.
 +
In these two talks we discuss a recent joint work with Michael Christ
 +
on a variant of the triangular Hilbert transform involving curvature.
 +
This object is closely related to the bilinear Hilbert transform with
 +
curvature and a maximally modulated singular integral of Stein-Wainger
 +
type. As an application we also discuss a quantitative nonlinear Roth
 +
type theorem on patterns in the Euclidean plane.
 +
The second talk will focus on the proof of a key ingredient, a certain
 +
regularity estimate for a local operator.
  
===Polona Durcik===
+
===Andrew Zimmer===
  
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''
+
Title:  Complex analytic problems on domains with good intrinsic geometry
  
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.
+
Abstract: In this talk, I will describe a new class of domains in complex Euclidean space which is defined in terms of the existence of a Kaehler metric with good geometric properties. This class is invariant under biholomorphism and includes many well-studied classes of domains such as strongly pseudoconvex domains, finite type domains in dimension two, convex domains, homogeneous domains, and embeddings of Teichmuller spaces. Further, certain analytic problems are tractable for domains in this family even when the boundary is non-smooth. In particular, it is possible to characterize the domains in this family where the dbar-Neumann operator on (0, q)-forms is compact (which generalizes an old result of Fu-Straube for convex domains).
  
 +
===Hong Wang===
  
===Song-Ying Li===
+
Title: Improved decoupling for the parabola
  
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''
+
Abstract: In 2014, Bourgain and Demeter proved the  $l^2$ decoupling estimates for the paraboloid with constant $R^{\epsilon}$. 
 +
We prove an $(l^2, L^6)$ decoupling inequality for the parabola with constant $(\log R)^c$.  This is joint work with Larry Guth and Dominique Maldague.
  
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates
+
===Kevin Luli===
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.
 
  
 +
Title: Smooth Nonnegative Interpolation
  
===Hanlong Fan===
+
Abstract: Suppose E is an arbitrary subset of R^n. Let f: E  \rightarrow [0, \infty). How can we decide if f extends to a nonnegative function C^m function F defined on all of R^n? Suppose E is finite. Can we compute a nonnegative C^m function F on R^n that agrees with f on E with the least possible C^m norm? How many computer operations does this take? In this talk, I will explain recent results on these problems. Non-negativity is one of the most important shape preserving properties for interpolants. In real life applications, the range of the interpolant is imposed by nature. For example, probability density, the amount of snow, rain, humidity, chemical concentration are all nonnegative quantities and are of interest in natural sciences. Even in one dimension, the existing techniques can only handle nonnegative interpolation under special assumptions on the data set. Our results work without any assumptions on the data sets.
  
''A generalization of the theorem of Weil and Kodaira on prescribing residues''
+
===Niclas Technau===
  
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: Number theoretic applications of oscillatory integrals
  
===Kyle Hambrook===
+
Abstract: We discuss how the analysis of oscillatory integrals can be used to solve number theoretic problems. More specifically, the focus will be on understanding fine-scale statistics of sequences on the unit circle. Further, we shall briefly explain a connection to quantum chaos.
  
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''
+
===Terence Harris===
  
I will discuss my recent work on some problems concerning
+
Title: Low dimensional pinned distance sets via spherical averages
Fourier decay and Fourier restriction for fractal measures on curves.
 
  
===Laurent Stolovitch===
+
Abstract: An inequality is derived for the average t-energy of weighted pinned distance measures, where 0 < t < 1, in terms of the L^2 spherical averages of Fourier transforms of measures. This generalises the result of Liu (originally for Lebesgue measure) to pinned distance sets of dimension smaller than 1, and strengthens Mattila's result from 1987, originally for the full distance set.
  
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''
+
===Name===
  
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
  
 +
Abstract
  
===Brian Cook===
+
===Name===
  
''Equidistribution results for integral points on affine homogenous algebraic varieties''
+
Title
  
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
  
===Shaoming Guo===
+
===Name===
  
''Polynomial Roth theorems in Salem sets''
+
Title
  
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.
+
Abstract
  
===Dean Baskin===
+
=Extras=
 +
[[Blank Analysis Seminar Template]]
  
''Radiation fields for wave equations''
 
  
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.
+
Graduate Student Seminar:
  
===Lillian Pierce===
+
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
 
 
''Short character sums''
 
 
 
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.
 
 
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 

Latest revision as of 12:23, 22 October 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. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier, or on different days, to accomodate speakers).

Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230

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 Dirac inner functions
September 29 Joris Roos University of Massachusetts - Lowell A triangular Hilbert transform with curvature, I
Wednesday September 30, 4 p.m. Polona Durcik Chapman University A triangular Hilbert transform with curvature, II
October 6 Andrew Zimmer UW Madison Complex analytic problems on domains with good intrinsic geometry
October 13 Hong Wang Princeton/IAS Improved decoupling for the parabola
October 20 Kevin Luli UC Davis Smooth Nonnegative Interpolation
October 21, 4.00 p.m. Niclas Technau UW Madison Number theoretic applications of oscillatory integrals
October 27 Terence Harris Cornell University Low dimensional pinned distance sets via spherical averages
Monday, November 2, 4 p.m. Yuval Wigderson Stanford University Title
November 10 Óscar Domínguez Universidad Complutense de Madrid Title
November 17 Tamas Titkos BBS U of Applied Sciences and Renyi Institute Title
November 24 Shukun Wu University of Illinois (Urbana-Champaign) Title
December 1 Jonathan Hickman The University of Edinburgh Title
December 8 Alejandra Gaitán Purdue University Title
February 2 Jongchon Kim UBC Title
February 9 Bingyang Hu Purdue University Title
February 16 Krystal Taylor The Ohio State University Title
February 23 Dominique Maldague MIT Title
March 2 Diogo Oliveira e Silva University of Birmingham Title
March 9 Title
March 16 Ziming Shi Rutgers University Title
March 23 Title
March 30 Title
April 6 Title
April 13 Title
April 20 Title
April 27 Title
May 4 Title

Abstracts

Alexei Poltoratski

Title: Dirac inner functions

Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations. We will discuss connections between problems in complex function theory, spectral and scattering problems for differential operators and the non-linear Fourier transform.

Polona Durcik and Joris Roos

Title: A triangular Hilbert transform with curvature, I & II.

Abstract: The triangular Hilbert is a two-dimensional bilinear singular originating in time-frequency analysis. No Lp bounds are currently known for this operator. In these two talks we discuss a recent joint work with Michael Christ on a variant of the triangular Hilbert transform involving curvature. This object is closely related to the bilinear Hilbert transform with curvature and a maximally modulated singular integral of Stein-Wainger type. As an application we also discuss a quantitative nonlinear Roth type theorem on patterns in the Euclidean plane. The second talk will focus on the proof of a key ingredient, a certain regularity estimate for a local operator.

Andrew Zimmer

Title: Complex analytic problems on domains with good intrinsic geometry

Abstract: In this talk, I will describe a new class of domains in complex Euclidean space which is defined in terms of the existence of a Kaehler metric with good geometric properties. This class is invariant under biholomorphism and includes many well-studied classes of domains such as strongly pseudoconvex domains, finite type domains in dimension two, convex domains, homogeneous domains, and embeddings of Teichmuller spaces. Further, certain analytic problems are tractable for domains in this family even when the boundary is non-smooth. In particular, it is possible to characterize the domains in this family where the dbar-Neumann operator on (0, q)-forms is compact (which generalizes an old result of Fu-Straube for convex domains).

Hong Wang

Title: Improved decoupling for the parabola

Abstract: In 2014, Bourgain and Demeter proved the $l^2$ decoupling estimates for the paraboloid with constant $R^{\epsilon}$. We prove an $(l^2, L^6)$ decoupling inequality for the parabola with constant $(\log R)^c$. This is joint work with Larry Guth and Dominique Maldague.

Kevin Luli

Title: Smooth Nonnegative Interpolation

Abstract: Suppose E is an arbitrary subset of R^n. Let f: E \rightarrow [0, \infty). How can we decide if f extends to a nonnegative function C^m function F defined on all of R^n? Suppose E is finite. Can we compute a nonnegative C^m function F on R^n that agrees with f on E with the least possible C^m norm? How many computer operations does this take? In this talk, I will explain recent results on these problems. Non-negativity is one of the most important shape preserving properties for interpolants. In real life applications, the range of the interpolant is imposed by nature. For example, probability density, the amount of snow, rain, humidity, chemical concentration are all nonnegative quantities and are of interest in natural sciences. Even in one dimension, the existing techniques can only handle nonnegative interpolation under special assumptions on the data set. Our results work without any assumptions on the data sets.

Niclas Technau

Title: Number theoretic applications of oscillatory integrals

Abstract: We discuss how the analysis of oscillatory integrals can be used to solve number theoretic problems. More specifically, the focus will be on understanding fine-scale statistics of sequences on the unit circle. Further, we shall briefly explain a connection to quantum chaos.

Terence Harris

Title: Low dimensional pinned distance sets via spherical averages

Abstract: An inequality is derived for the average t-energy of weighted pinned distance measures, where 0 < t < 1, in terms of the L^2 spherical averages of Fourier transforms of measures. This generalises the result of Liu (originally for Lebesgue measure) to pinned distance sets of dimension smaller than 1, and strengthens Mattila's result from 1987, originally for the full distance set.

Name

Title

Abstract

Name

Title

Abstract

Name

Title

Abstract

Extras

Blank Analysis Seminar Template


Graduate Student Seminar:

https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html