Semiclassical Measures for Laplacian Eigenfunctions and Quantum Cat Maps

Explore a lecture from the first ZhengTong Chern-Weil Symposium in Mathematics, featuring MIT's Semyon Dyatlov discussing "Semiclassical Measures for Laplacian Eigenfunctions and Quantum Cat Maps." Delve into the world of quantum chaos, focusing on semiclassical measures and their role in capturing macroscopic behavior of eigenfunction sequences in high energy limits. Examine the supports of semiclassical measures for Laplacian eigenfunctions and quantum cat maps, with particular emphasis on negatively curved surfaces. Learn about the fractal uncertainty principle and its applications in proving full support properties. Discover the challenges in extending these results to higher dimensions and the alternative approaches used for higher dimensional quantum cat maps. Gain insights into joint work with Jin, Nonnenmacher, Bourgain, and Jézéquel, exploring the interplay between mathematics and quantum mechanics in this hour-long presentation from the University of Chicago Department of Mathematics.