Quantum limits of sub-Riemannian manifolds

Jeudi 4 juin 11:00-12:00 - Cyril Letrouit - ENS

Résumé : Riemannian geometry, the distribution on the manifold of high-frequency eigenfunctions of the Laplace-Beltrami operator heavily depends on the properties of the geodesic flow : if it is ergodic, nearly all eigenfunctions are equidistributed, whereas eigenfunctions of completely integrable systems, due to the high multiplicity of some eigenvalues, may present more complicated patterns. In this talk, we deal with the same problem in the more general framework of sub-Riemannian geometry, for which one of the standard examples is the sub-Laplacian in R^3 or in one of its compact quotients. The associated geodesic flow is completely integrable, and the study of the so-called Quantum Limits, which characterize possible limits of eigenfunctions, reveals a very rich structure, in which an in-nite number of flows comes into play.

Notes de dernières minutes : Lien BBB : https://bbb.imo.universite-paris-saclay.fr/b/nic-av7-y4q

Quantum limits of sub-Riemannian manifolds  Version PDF