Mathematics Department Colloquium: What is quantum chaos?

Colloquium | November 16 | 4:10-5 p.m. | 60 Evans Hall

 Semyon Dyatlov, UC Berkeley

 Department of Mathematics

Where do eigenfunctions of the Laplacian concentrate as eigenvalues go to infinity? Do they equidistribute or do they concentrate in an uneven way? It turns out that the answer depends on the nature of the geodesic flow. I will discuss various results in the case when the flow is chaotic: the Quantum Ergodicity theorem of Shnirelman, Colin de Verdière, and Zelditch, the Quantum Unique Ergodicity conjecture of Rudnick–Sarnak, the progress on it by Lindenstrauss and Soundararajan, and the entropy bounds of Anantharaman–Nonnenmacher. I will conclude with a recent lower bound on the mass of eigenfunctions obtained with Jin. It relies on a new tool called “fractal uncertainty principle” developed in the works with Bourgain and Zahl.

 ribet@berkeley.edu