# Difference between revisions of "Fall 2021 and Spring 2022 Analysis Seminars"

Fall 2019 and Spring 2020 Analysis Seminar Series

The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.

# Analysis Seminar Schedule

 date speaker title host(s) institution 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 An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ 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 Diogo Oliveira e Silva University of Birmingham Title Betsy Apr 28 No Seminar

# Abstracts

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.

### Xiaocheng Li

Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$

Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.

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