The Support of Semiclassical Measures in Higher Dimensions

This lecture from the Joint IAS/PU Groups and Dynamics Seminar explores semiclassical measures for Laplace eigenfunctions on compact hyperbolic n-manifolds, motivated by the quantum unique ergodicity conjecture. Learn how the support of these measures must contain the cosphere bundle of a compact immersed totally geodesic submanifold. Follow along as Elena Kim from MIT adapts a 2-dimensional argument by Dyatlov and Jin to higher dimensions using Cohen's higher-dimensional fractal uncertainty principle. The presentation includes work on the toy model of quantum cat maps to illustrate key proof ideas. This research represents joint work with Nick Miller and will be presented on March 11, 2025, at 4:30pm in Simonyi 101.