Local Mixing of Diagonal Flows on Anosov Homogeneous Spaces

Explore a 58-minute lecture on local mixing of diagonal flows on Anosov homogeneous spaces, presented by Pratyush Sarkar from UC San Diego at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the extension of Winter's mixing results for convex cocompact rank one locally symmetric spaces to higher rank Lie groups. Examine the joint work with Michael Chow, which proves local mixing of one-parameter diagonal flows on Anosov homogeneous spaces. Discover applications of these mixing results in counting, equidistribution, and decay of matrix coefficients. Learn about the challenges posed by infinite Bowen-Margulis-Sullivan measures in Anosov subgroups of higher rank Lie groups and the need for local mixing analysis. Gain insights into recent developments, including Chow-Fromm's findings on joint equidistribution of maximal flat cylinders and holonomies.