Scaling asymptotics for Szego kernels on Grauert tubes
组织者
陈曦
,
金龙
演讲者
Robert Chang
时间
2022年01月07日 10:00 至 11:00
地点
1129B
线上
Zoom 638 227 8222
(BIMSA)
摘要
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).