Analysis Seminar

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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 UW 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 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 A generalization of the theorem of Weil and Kodaira on prescribing residues Brian
Monday, Nov. 12, B139 Kyle Hambrook San Jose State University Fourier Decay and Fourier Restriction for Fractal Measures on Curves Andreas
Nov 13 Laurent Stolovitch Université de Nice - Sophia Antipolis Equivalence of Cauchy-Riemann manifolds and multisummability theory Xianghong
Nov 20 Grad Student Seminar
Nov 27 No Seminar Title
Dec 4 No Seminar Title
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 Shaoming Guo UW Madison Title
Feb 26 Person Institution Title Sponsor
Mar 5 Person Institution Title Sponsor
Mar 12 No Seminar Title
Mar 19 Spring Break!!!
Mar 26 Person Institution Title Sponsor
Apr 2 Stefan Steinerberger Yale Title Shaoming, Andreas
Apr 9 Franc Forstnerič Unversity of Ljubljana Title Xianghong, Andreas
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.



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.

Kyle Hambrook

Fourier Decay and Fourier Restriction for Fractal Measures on Curves

I will discuss my recent work on some problems concerning Fourier decay and Fourier restriction for fractal measures on curves.

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