Fall 2021 and Spring 2022 Analysis Seminars
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
Analysis Seminar Schedule
|Sept 11||Simon Marshall||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|
|Nov 6||Hanlong Fang||UW Madison||Title||Brian|
|Monday, Nov. 12||Kyle Hambrook||San Jose State University||Title||Andreas|
|Nov 13||Laurent Stolovitch||Université de Nice - Sophia Antipolis||Equivalence of Cauchy-Riemann manifolds and multisummability theory||Xianghong|
|Nov 20||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|
|Mar 12||No Seminar||Title|
|Mar 19||Spring Break!!!|
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.
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.
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.
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.
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.