Monday, November 1, 2021
11/01/2021 - 10:15am
A famous theorem due to Hopf-Tsuji-Sullivan-Kaimanovich asserts that the geodesic flow and the Brownian motion on a rank-one symmetric space of the non-compact type $\Lambda \backslash G/K$ are either both recurrent ergodic or both transient. In this talk, I will explain how this dichotomy can be extended to a much larger class of random walks, namely any right random walk on $\Lambda \backslash G$ induced by a Zariski-dense probability measure on $G$ with finite first moment.
11/01/2021 - 4:30pm
Abstract: The notion of a "t-structure on a triangulated category" was introduced around 1980. The notion of "co-t-structure" could have been defined back then as well, but it didn't receive much attention until the past 10 years or so, probably because it wasn't clear what it was good for. I'll explain these notions and give some elementary examples. I will then discuss some "modern" examples of co-t-structures in geometric representation theory. In particular, I will explain a remarkable new co-t-structure on the derived category of coherent sheaves on the nilpotent cone of a reductive group. The study of this co-t-structure leads to the proof of the Humphreys conjecture on tilting modules for a reductive group. This is joint work with W. Hardesty.
Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.