The Support of Semiclassical Measures in Higher Dimensions

Motivated by the quantum unique ergodicity conjecture, we examine semiclassical measures for Laplace eigenfunctions on compact hyperbolic n

-manifolds. We prove their support must contain the cosphere bundle of a compact immersed totally geodesic submanifold.

The proof adapts a 2-dimensional argument by Dyatlov and Jin to higher dimensions using Cohen's higher-dimensional fractal uncertainty principle. To explain some of the main proof ideas, we will present work on the toy model of quantum cat maps.

This is joint work with Nick Miller.