Title: What is quantum chaos?
Speaker: Semyon Dyatlov
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, Zelditch, and Colin de Verdi\`ere, 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 recent lower bounds on the mass of eigenfunctions obtained with Jin and Nonnenmacher. They rely on a new tool called "fractal uncertainty principle" developed in the works with Bourgain and Zahl.Date: Wednesday, May 22, 2019