Title: Quantum ergodicity and subriemannian geometry
Speaker: Luc Hillairet
Speaker Info: University of Orléans
Quantum ergodicity is related to how the eigenfunctions of a given operator concentrate as the eigenvalue grows. It is a celebrated result of Shnirelman, Zelditch, Colin de Verdière that it holds for the Riemannian Laplacian on a compact manifold provided that the geodesic flow is ergodic. We address this question in the subriemannian setting of a contact 3D structure. Several new steps have to be added to the usual proof to deal with the hypoelliptic nature of the corresponding Laplacian.Date: Monday, May 1, 2017
Joint work with Y. Colin de Verdière and E. Trélat.