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'''Analysis Seminar
 
'''
 
[http://www.math.wisc.edu/~seeger/curr.html Current Semester]
 
  
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 Andreas at seeger(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 Spring 2017 =
+
 
 +
 
 +
=[[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   
 
!align="left" | speaker
 
!align="left" | speaker
 +
|align="left" | '''institution'''
 
!align="left" | title
 
!align="left" | title
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|January 17, Math Department Colloquium
+
|September 22
| Fabio Pusateri (Princeton)  
+
|Alexei Poltoratski
|[[#Fabio Pusateri   |  The Water Waves Problem ]]
+
|UW Madison
| Sigurd Angenent
+
|[[#Alexei Poltoratski  |  Dirac inner functions ]]
|
+
|
 +
|-
 +
|September 29
 +
|Joris Roos
 +
|University of Massachusetts - Lowell
 +
|[[#Polona Durcik and Joris Rooslinktoabstract  |  A triangular Hilbert transform with curvature, I ]]
 +
|
 +
|-
 +
|Wednesday September 30, 4 p.m.
 +
|Polona Durcik
 +
|Chapman University
 +
|[[#Polona Durcik and Joris Roos  |  A triangular Hilbert transform with curvature, II ]]
 +
|
 +
|-
 +
|October 6
 +
|Andrew Zimmer
 +
|UW Madison
 +
|[[#Andrew Zimmer  |  Complex analytic problems on domains with good intrinsic geometry ]]
 +
|
 +
|-
 +
|October 13
 +
|Hong Wang
 +
|Princeton/IAS
 +
|[[#Hong Wang  |  Improved decoupling for the parabola ]]
 +
|
 +
|-
 +
|October 20
 +
|Kevin Luli
 +
|UC Davis
 +
|[[#Kevin Luli  |  Smooth Nonnegative Interpolation ]]
 +
|
 +
|-
 +
|October 21, 4.00 p.m.
 +
|Niclas Technau
 +
|UW Madison
 +
|[[#Niclas Technau  |  Number theoretic applications of oscillatory integrals ]]
 +
|
 +
|-
 +
|October 27
 +
|Terence Harris
 +
| Cornell University
 +
|[[#Terence Harris  |  Low dimensional pinned distance sets via spherical averages ]]
 +
|
 +
|-
 +
|Monday, November 2, 4 p.m.
 +
|Yuval Wigderson
 +
|Stanford  University
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|November 10
 +
|Óscar Domínguez
 +
| Universidad Complutense de Madrid
 +
|[[#linktoabstract  |  Title ]]
 +
|
 +
|-
 +
|November 17
 +
|Tamas Titkos
 +
|BBS U of Applied Sciences and Renyi Institute
 +
|[[#linktoabstract |  Title ]]
 +
|  
 +
|-
 +
|November 24
 +
|Shukun Wu
 +
|University of Illinois (Urbana-Champaign)
 +
||[[#linktoabstract  |   Title ]]
 +
|
 +
|-
 +
|December 1
 +
| Jonathan Hickman
 +
| The University of Edinburgh
 +
|[[#linktoabstract  Title ]]
 +
|  
 +
|-
 +
|December 8
 +
|Alejandra Gaitán
 +
| Purdue University
 +
|[[#linktoabstract  |  Title ]]
 +
|  
 
|-
 
|-
|January 24, Joint Analysis/Geometry Seminar
+
|February 2
| Tamás Darvas (Maryland)
+
|Jongchon Kim
|[[#Tamás Darvas | Existence of constant scalar curvature Kähler metrics and properness of the K-energy ]]
+
| UBC
| Jeff Viaclovsky
+
|[[#linktoabstract |   Title ]]
|
+
|  
 
|-
 
|-
|Monday, January 30, 3:30, VV901 (PDE Seminar)
+
|February 9
| Serguei Denissov (UW Madison)
+
|Bingyang Hu
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid ]]
+
|Purdue University
 +
|[[#linktoabstract |   Title ]]
 
|  
 
|  
 
|-
 
|-
|February 7
+
|February 16
| Andreas Seeger (UW Madison)
+
|Krystal Taylor
|[[#Andreas SeegerThe Haar system in Sobolev spaces]]
+
|The Ohio State University
 +
|[[#linktoabstract  Title ]]
 
|
 
|
 
|-
 
|-
|February 21
+
|February 23
| Jongchon Kim (UW Madison)
+
|Dominique Maldague
|[[#Jongchon Kim Some remarks on Fourier restriction estimates ]]
+
|MIT
| Andreas Seeger
+
|[[#linktoabstract  Title ]]
 +
|
 
|-
 
|-
|March 7, Mathematics Department Distinguished Lecture
+
|March 2
| Roger Temam (Indiana) 
+
|Diogo Oliveira e Silva
|[[#Roger Temam (Colloquium) | On the mathematical  modeling of the humid atmosphere   ]]
+
|University of Birmingham
| Leslie Smith
+
|[[#linktoabstract Title ]]
 +
|
 
|-
 
|-
|Wednesday, March 8, Joint Applied Math/PDE/Analysis  Seminar
+
|March 9
| Roger Temam (Indiana) 
+
|
|[[#Roger Temam (Seminar) Weak solutions of the Shigesada-Kawasaki-Teramoto system]]
+
|
| Leslie Smith
+
|[[#linktoabstract Title ]]
 +
|
 
|-
 
|-
|March 14
+
|March 16
| Xianghong Chen (UW Milwaukee)
+
|Ziming Shi
|[[#Xianghong Chen  Restricting the Fourier transform to some oscillating curves ]]
+
|Rutgers University
| Andreas Seeger
+
|[[#linktoabstract  Title ]]
 
|
 
|
 
|-
 
|-
|March 21
+
|March 23
| SPRING BREAK
+
|
|[[#linktoabstract | ]]
+
|
 
+
|[[#linktoabstract |   Title ]]
 
+
|
 
|-
 
|-
|Monday, March 27 (joint PDE/Analysis Seminar), 3:30, VV901
+
|March 30
| Sylvia Serfaty (NYU)
+
|
|[[#Sylvia Serfaty |Mean Field Limits for Ginzburg Landau Vortices ]]
+
|
| Hung Tran
+
|[[#linktoabstract  |   Title ]]
 
|
 
|
 
|-
 
|-
|March 28
+
|April 6
| Brian Cook (Fields Institute)
+
|
|[[#Brian Cook |Twists on the twisted ergodic theorems ]]
+
|
| Andreas Seeger
+
|[[#linktoabstract  |   Title ]]
 
|
 
|
 
|-
 
|-
|Friday, March 31, 4:00 p.m., B139
+
|April 13
| Laura Cladek (UBC)
+
|
|[[#Laura Cladek | Endpoint bounds for the lacunary spherical maximal operator ]]
+
|
| Andreas Seeger
+
|[[#linktoabstract  |   Title ]]
 
|
 
|
 
|-
 
|-
|April 4
+
|April 20
| Francesco Di Plinio (Virginia)
+
|
|[[#Francesco di Plinio Sparse domination of singular integral operators ]]
+
|
| Andreas Seeger
+
|[[#linktoabstract  Title ]]
 
|
 
|
 
|-
 
|-
|April 11
+
|April 27
| Xianghong Gong (UW Madison)
+
|
|[[#linktoabstract  |  TBA ]]
+
|
|
+
|[[#linktoabstract  |  Title ]]
 
|
 
|
 
|-
 
|-
|April 25 (joint PDE/Analysis Seminar)
+
|May 4
| Chris Henderson (University of Chicago)
+
|
|[[#linktoabstract  |  TBA ]]
+
|
| Jessica Lin
+
|[[#linktoabstract  |  Title ]]
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
 +
===Alexei Poltoratski===
  
===  Fabio Pusateri  ===
+
Title: Dirac inner functions
''The Water Waves problem''
 
  
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.
+
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.
  
===   Tamás Darvas ===
+
===Polona Durcik and Joris Roos===
''Existence of constant scalar curvature Kähler metrics and properness of the K-energy''
 
  
Given a compact Kähler manifold $(X,\omega)$, we show that if there exists a constant
+
Title: A triangular Hilbert transform with curvature, I & II.
scalar curvature Kähler metric  cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an
 
appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful
 
study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is
 
joint work with Robert Berman and Chinh H. Lu.
 
  
=== Serguei Denissov  ===
+
Abstract: The triangular Hilbert is a two-dimensional bilinear singular
''Instability in 2D Euler equation of incompressible inviscid fluid''
+
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.
  
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.
+
===Andrew Zimmer===
  
=== Andreas Seeger ===
+
Title: Complex analytic problems on domains with good intrinsic geometry
''The Haar system in Sobolev spaces''
 
  
We consider the Haar system on  Sobolev  spaces and ask:
+
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).
When is it a Schauder basis?
 
When is it an unconditional  basis?
 
Some answers are given in recent joint work Tino Ullrich and Gustavo Garrigós.
 
  
=== Jongchon Kim  ===
+
===Hong Wang===
''Some remarks on Fourier restriction estimates''
 
  
The Fourier restriction problem, raised by Stein in the 1960’s, is a hard open problem in harmonic analysis. Recently, Guth made some impressive progress on this problem using polynomial partitioning, a divide and conquer technique developed by Guth and Katz for some problems in incidence geometry.
+
Title: Improved decoupling for the parabola
In this talk, I will introduce the restriction problem and the polynomial partitioning method. In addition, I will present some sharp L^p to L^q estimates for the Fourier extension operator that use an estimate of Guth as a black box.
 
  
=== Roger Temam (Colloquium) ===
+
Abstract: In 2014, Bourgain and Demeter proved the  $l^2$ decoupling estimates for the paraboloid with constant $R^{\epsilon}$. 
''On the mathematical  modeling of the humid atmosphere''
+
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.
  
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase  due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.
+
===Kevin Luli===
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.
 
 
=== Roger Temam (Seminar) ===
 
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''
 
  
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.
+
Title: Smooth Nonnegative Interpolation
Based on an article with Du Pham, to appear in Nonlinear Analysis.
 
  
===  Xianghong Chen ===
+
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.
''Restricting the Fourier transform to some oscillating curves''
 
  
I will talk about Fourier restriction to some compact smooth curves. The problem is relatively well understood for curves with nonvanishing torsion due to work of Drury from the 80's, but is less so for curves that contain 'flat' points (i.e. vanishing torsion). Sharp results are known for some monomial-like or finite type curves by work of Bak-Oberlin-Seeger, Dendrinos-Mueller, and Stovall, where a geometric inequality (among others) plays an important role. Such an inequality fails to hold if the torsion demonstrates strong sign-changing behavior, in which case endpoint restriction bounds may fail. In this talk I will present how one could obtain sharp non-endpoint results for certain space curves of this kind. Our approach uses a covering lemma for smooth functions that strengthens a variation bound of Sjolin, who used it to obtain a similar result for plane curves. This is joint work with Dashan Fan and Lifeng Wang.
+
===Niclas Technau===
  
===Sylvia Serfaty ===
+
Title: Number theoretic applications of oscillatory integrals
  
''Mean Field Limits for Ginzburg Landau Vortices''
+
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.
  
Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.
+
===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.
  
=== Brian Cook ===
+
===Name===
''Twists on the twisted ergodic theorems''
 
  
The classical pointwise ergodic theorem has been adapted to include averages twisted by a phase polynomial, primary examples being the ergodic theorems of Wiener-Wintner and Lesigne. Certain uniform versions of these results are also known. Here uniformity refers to the collection of polynomials of degree less than some prescribed number. In this talk we wish to consider weakening the hypothesis in these latter results by considering uniformity over a smaller class of polynomials, which is naturally motivated when considering certain applications related to the circle method.
+
Title
  
 +
Abstract
  
=== Francesco di Plinio ===
+
===Name===
  
''Sparse domination of singular integral operators''
+
Title
  
Singular integral operators, which are a priori signed and non-local, can be dominated  in norm, pointwise, or dually, by sparse averaging operators,  which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather immediate estimates for the averaging operators.  In this talk, we present several positive sparse domination results of singular integrals falling beyond the scope of classical Calderón-Zygmund theory; notably, modulation invariant multilinear singular integrals including the bilinear Hilbert transforms, variation norm Carleson operators, matrix-valued kernels, rough homogeneous singular integrals and critical Bochner-Riesz means, and singular integrals along submanifolds with curvature.  Collaborators:  Amalia Culiuc, Laura Cladek, Jose Manuel Conde-Alonso, Yen Do, Yumeng Ou and Gennady Uraltsev.
+
Abstract
  
=== Laura Cladek ===
+
===Name===
  
''Endpoint bounds for the lacunary spherical maximal operator''
+
Title
  
Define the lacunary spherical maximal operator as the maximal operator corresponding to averages over spheres of radius 2^k for k an integer. This operator may be viewed as a model case for studying more general classes of singular maximal operators and Radon transforms. It is a classical result in harmonic analysis that this operator is bounded on L^p for p>1, but the question of weak-type (1, 1) boundedness (which would correspond to pointwise convergence of lacunary spherical averages for functions in L1) has remained open. Although this question still remains open, we discuss some new endpoint bounds for the operator near L1 that allows us to conclude almost everywhere pointwise convergence of lacunary spherical means for functions in a slightly smaller space than L\log\log\log L. This is based on joint work with Ben Krause.
+
Abstract
  
 
=Extras=
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 
[[Blank Analysis Seminar Template]]
 +
 +
 +
Graduate Student Seminar:
 +
 +
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html

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