EVENT DETAILS AND ABSTRACT

Title: Quantum ergodicity in the Benjamini-Schramm limit on higher rank real and p-adic locally symmetric spaces
Speaker: Carsten Peterson
Speaker Info: Paderborn University
Brief Description:
Special Note:
Abstract:

Originally, quantum ergodicity concerned equidistribution properties of Laplacian eigenfunctions with large eigenvalue on manifolds for which the geodesic flow is ergodic. More recently, several authors have investigated quantum ergodicity for sequences of spaces which “converge” to their common universal cover and when one restricts to eigenfunctions with eigenvalues in a fixed range. Previous authors have considered this type of quantum ergodicity in the settings of regular graphs, rank one locally symmetric spaces, and some higher rank locally symmetric spaces. We prove analogous results in the case when the underlying common universal cover is the Bruhat-Tits building associated to PGL(3, F) where F is a non-archimedean local field. This may be seen as both a higher rank analogue of the regular graphs setting as well as a non-archimedean analogue of the symmetric space setting. We shall also mention ongoing joint work with Farrell Brumley, Simon Marshall, and Jasmin Matz dealing further with higher rank locally symmetric spaces.