Seminar Event Detail


Geometry

Date:  Friday, April 15, 2022
Location:  3866 East Hall (4:00 PM to 5:00 PM)

Title:  On quantum ergodicity on Bruhat-Tits buildings

Abstract:   Quantum ergodicity refers to equidistribution of eigenfunctions of Laplace-like operators which arise from ``quantizing'' an ergodic dynamical system. The original quantum ergodicity theorem was about eigenfunctions of the Laplacian in the high eigenvalue limit on a manifold with ergodic geodesic flow (such as a hyperbolic surface). More recently Anantharaman and Le Masson studied eigenfunctions of the adjacency operator on sequences of regular graphs Benjamini-Schramm converging to the tree. Inspired by these results, Le Masson and Sahlsten obtained analogous results for sequences of hyperbolic surfaces Benjamini-Schramm converging to the hyperbolic plane, and Brumley and Matz for sequences of locally symmetric spaces Benjamini-Schramm converging to the symmetric space SL(n, R)/SO(n). By reinterpreting (certain) regular graphs as quotients of the Bruhat-Tits building associated to SL(2, F), where F is a p-adic field, a natural question is if analogous results hold for quotients of higher rank Bruhat-Tits buildings (which may be viewed as p-adic symmetric spaces). We obtain analogous results for the Bruhat-Tits building associated to SL(3, F). No prior background on quantum ergodicity or buildings will be assumed in this talk.

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Speaker:  Carsten Peterson
Institution:  U Michigan

Event Organizer:   Spatzier   

 

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