Mesures semiclassiques sur surfaces hyperboliques

Jeudi 1er juin 2017 15:45-16:45 - Semyon Dyatlov - MIT

Résumé : On a compact hyperbolic surface, a semiclassical measure is an invariant probability measure on the cosphere bundle which arises as the high frequency limit of a sequence of eigenfunctions of the Laplacian. The quantum unique ergodicity conjecture states that the only such measure is the Liouville measure, however so far it has only been established in the very algebraically special case of the modular surface.
I will present a new restriction on semiclassical measures : their support equals the entire cosphere bundle. The key new ingredient is a fractal uncertainty principle, stating that no function can be localized close to a porous set in both position and frequency. This talk is based on joint works with Long Jin and with Jean Bourgain.

Lieu : Bât 425, salle 113-115

Mesures semiclassiques sur surfaces hyperboliques  Version PDF