researchseminars.org

Jasmin Matz (Copenhagen)
2021-10-29 16:30 - 17:30 UTC | https://researchseminars.org/talk/HASS21/10/
Title: Quantum ergodicity in the level aspect (https://researchseminars.org/talk/HASS21/10/)
by Jasmin Matz (Copenhagen) as part of Harmonic Analysis and Symmetric Spaces 2021

Abstract
A classical result of Shnirelman and others shows that closed Riemannian manifolds of negative curvature are quantum ergodic, meaning that on average the probability measures $|f|^2 dx$ on $M$, with $f$ running through normalized Laplace eigenfunctions on $M$ with growing eigenvalue, converge towards the Riemannian measure $dx$ on $M$.

Following ideas of Abert, Bergeron, Le Masson, and Sahlsten, we look at a related situation: We want to consider certain sequences of manifolds together with Laplace eigenfunctions of approximately the same eigenvalue instead of high energy eigenfunctions on a fixed manifold. In my talk I want to discuss joint work with F. Brumley in which we study this situation in higher rank for sequences of compact quotients of $SL(n,\mathbb{R})/SO(n)$.
