The University of Arizona

What is Quantum Chaos?

What is Quantum Chaos?

Series: Mathematics Colloquium
Location: Math 501
Presenter: Semyon Dyatlov, Massachusetts Institute of Technology

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 Verdi\`ere, 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.

Refreshments in Math Commons Room at 3:30pm

Department of Mathematics, The University of Arizona 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089 USA Voice: (520) 621-6892 Fax: (520) 621-8322 Contact Us © Copyright 2017 Arizona Board of Regents All rights reserved