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Seminar on microlocal analysis and applications
Seminar on microlocal analysis and applications
Scaling asymptotics for Szego kernels on Grauert tubes
Scaling asymptotics for Szego kernels on Grauert tubes
Organizers
Xi Chen
,
Long Jin
Speaker
Robert Chang
Time
Friday, January 7, 2022 10:00 AM - 11:00 AM
Venue
1129B
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The Grauert tube of a real analytic manifold is a strongly pseudoconvex domain whose defining function is derived from the Riemannian metric . In fact, is diffeomorphic to the co-ball bundle under the complexified exponential map. Grauert tubes therefore offer a bridge between the setting of geometric quantization (where the dual circle bundle is a strongly pseudoconvex domain) and the setting of standard quantization on Riemannian manifold.
In this talk, I will focus on analysis on Grauert tubes and present a recent joint work with Abe Rabinowitz (Northwestern University) on near-diagonal scaling asymptotics for the Szego kernel. As an application, we obtain sharp norm estimates on complexified Laplace eigenfunctions (Husimi distributions).