Speaker: Xiaoqi Huang, Louisiana State University

Time: 9:00-10:00 a.m., Apr 30, 2025, GMT+8

Venue: Online: Zoom ID: 870 5684 4637 Password: 490964

Abstract: 

We will first discuss the relation between curvature and L^q norm estimates of spectral projection operators on compact manifolds.In particular, we will demonstrate that the sign of the curvature of a compact space form can be inferred from the growth rate of L^q-norms of L^2-normalized quasimodes. We will also discuss related recent work on the sharp spectral projection estimates on noncompact asymptotically hyperbolic surfaces with negative curvature, including all convex cocompact hyperbolic surfaces.This is based on joint works with Christopher Sogge, Zhongkai Tao and Zhexing Zhang.

Source: School of Mathematical Sciences, PKU