EVENT DETAILS AND ABSTRACT

Title: Quantum ergodicity on riemannian manifolds
Speaker: Nalini Anantharaman
Speaker Info: Université de Strasbourg
Brief Description:
Special Note:
Abstract:

"Quantum ergodicity" in the traditional sense deals with the question of (de)localization of eigenfunctions of the laplacian on a Riemannian manifold, in the limit of high eigenvalues. In this "semiclassical limit", it is known that the behavior of eigenfunctions bears some relation with the ergodic properties of a dynamical system called the "geodesic flow". TALK 1 will present a survey of this topic.

In TALK 2, we will move to the less developed subject of quantum ergodicity on graphs. In this talk, we consider finite regular graphs whose size grows to infinity, and discuss some delocalization results for eigenfunctions of the adjacency matrix (joint w. Le Masson). We will also discuss connections between QE on graphs and QE on manifolds, mostly through the work of Lindentrauss and collaborators on "arithmetic" quantum ergodicity.

TALK 3: Results on QE on discrete graphs are so far restricted to regular graphs (for which all points have the same number of neighbours). Here we will discuss new proofs of QE, and other models to which we would like to apply them : Anderson model on regular graphs, percolation graphs on regular graphs. We will also put our results into perspective by comparing them to recent results on eigenvectors of random matrices.