Title: Quantum Ergodicity on Regular Graphs

Abstract: 
The quantum ergodicity theorem (Snirelman, Zelditch, Colin de Verdière) is a 
theorem about the eigenfunctions of the Laplacian on Riemannian manifolds with ergodic 
geodesic flow, stating that in the large eigenvalue limit they present some spatial 
equidistribution properties. These eigenfunctions can be seen as the states (wave functions) 
of a quantum system. 
We will present a version of the theorem for the discrete Laplacian on regular graphs 
(joint work with Nalini Anantharaman). Moreover, we will discuss a simplified approach based 
on a recent joint work with Shimon Brooks and Elon Lindenstrauss, where we also applied 
the ideas to special bases of eigenfunctions on the sphere.