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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).