Mathematics Colloquium
Xiaoqi Huang
Louisiana State University
Title:Curvature and sharp growth rates of log-quasimodes on compact manifolds
Date: Wednesday, March 6, 2024
Place and Time: Love 101, 3:05-3:55 pm
Abstract. We will discuss the relation between curvature and L^q norm estimates of spectral projection operators on compact manifolds. We will present a new way that one can hear the shape of a connected compact manifold of constant sectional curvatures, if the shape refers to curvature, and the radios used are the L^q norm of quasimodes. We will also discuss improved Strichartz estimates for solutions of the Schrodinger equation on compact manifolds under certain curvature assumptions.