Date: Friday, April 15, 2022
Location: 3866 East Hall (4:00 PM to 5:00 PM)
Title: On quantum ergodicity on BruhatTits buildings
Abstract: Quantum ergodicity refers to equidistribution of eigenfunctions of Laplacelike 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 BenjaminiSchramm converging to the tree. Inspired by these results, Le Masson and Sahlsten obtained analogous results for sequences of hyperbolic surfaces BenjaminiSchramm converging to the hyperbolic plane, and Brumley and Matz for sequences of locally symmetric spaces BenjaminiSchramm converging to the symmetric space SL(n, R)/SO(n). By reinterpreting (certain) regular graphs as quotients of the BruhatTits building associated to SL(2, F), where F is a padic field, a natural question is if analogous results hold for quotients of higher rank BruhatTits buildings (which may be viewed as padic symmetric spaces). We obtain analogous results for the BruhatTits 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
