Geometry Seminar

Date: October 2, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Boris Hanin, TAMU

Title: Pointwise Estimates in the Weyl Law on a Compact Manifold

Abstract: Let (M,g) be a compact smooth Riemannian manifold. This talk focuses on connecting the structure of geodesics on (M,g) to the behavior of eigenfunctions of the Laplacian at high frequencies. I will explain a physical heuristic for why such a connection should exist. I will then present some new estimates for the second term in the pointwise Weyl Law. These estimates imply that if the geodesics passing through a given point on M are dispersive (in a suitable sense), then the spectral projector of the Laplacian onto the frequency interval (lambda,lambda+1] has a universal scaling limit as lambda goes to infinity (depending only on the dimension of M). This is joint work with Y. Canzani.