Hebrew University topology and geometry seminar

Abstract: Every compact Riemannian manifold (M,g) is locally modeled on R^n in the sense that there exist coordinates near any point x in M so that the metric g coincides with the flat metric to first order. The purpose of this talk is to explain a new result, which shows that near any aperiodic point x in M, high frequency eigenfunctions of the Laplacian also exhibit a universal local behavior that depends only on the dimension of M. This result follows from a new estimate off the diagonal on the error term in the local Weyl law. This is joint is with Y. Canzani.