Monday, November 15, 2021
11/15/2021 - 4:00pm
Discrete subgroups of semisimple Lie groups arise in a variety of contexts, sometimes “in nature” as monodromy groups of families of manifolds, and other times in relation to geometric structures and associated dynamical systems. I will discuss a class of such discrete subgroups that come from certain variations of Hodge structure and give rise to Anosov representations. Among many consequences, this leads to uniformization results for certain domains of discontinuity of the discrete group, and also yields a proof of a conjecture of Eskin, Kontsevich, Moller, and Zorich on Lyapunov exponents. The necessary background will be explained.
11/15/2021 - 4:30pm
Abstract: Kazhdan-Lusztig polynomials are fascinating! In the 80s Lusztig and Dyer independently noticed that the Kazhdan-Lusztig polynomial for a pair x,y of elements in a Coxeter group appears to only depend on the isomorphism type of the interval [x,y] in Bruhat order. This statement became known as the combinatorial invariance conjecture. I will review this conjecture, and discuss what is known. I will present a conjecture which should lead to a proof when W is the symmetric group.
Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.