Joint IAS/PU Groups and Dynamics Seminar

A cornerstone of quantum chaos is the Quantum Ergodicity theorem, which states roughly that on a closed Riemannian manifold with ergodic geodesic flow the L2 mass of most Laplacian eigenfunctions equidistributes in the high frequency limit. An analogous question, where instead of the frequency it is the geometry which varies, was first considered by Anantharaman-Le Masson for eigenfunctions of large regular graphs, provided they converge, in a certain sense, to the regular tree, and have a uniform spectral gap. Several works have since proved Quantum Ergodicity in this large volume regime, most notably by Le Masson-Sahlsten in the setting of closed hyperbolic surfaces. In this talk, I will present joint work with Marshall, Matz, and Peterson, which extends the Quantum Ergodicity theorem to Benjamini-Schramm convergent sequences of general locally symmetric spaces.