Monday, October 25, 2021
10/25/2021 - 4:00pm
I will outline some ideas in recent work with D. Fisher and S. Hurtado establishing Zimmer’s conjecture for actions of general lattices in SL(n,R). This extends our earlier results for actions of cocompact lattices and of SL(n,Z). Problems involving escape of mass and “escape of Lyapunov exponents” arise when the lattice is not cocompact and I will outline some ideas used to avoid such behavior.
10/25/2021 - 4:30pm
Abstract: Let G and G’ be Langlands dual reductive groups (e.g. SL(n) and PGL(n)). According to a theorem by Donagi-Pantev, the generic fibres of the moduli spaces of G-Higgs bundles and G’-Higgs bundles are dual abelian varieties and are therefore derived equivalent. It is an interesting open problem to prove existence of a derived equivalence over the full Hitchin base. I will report on joint work in progress with Shiyu Shen, in which we construct a K-theoretic shadow thereof: natural equivalences between complex K-theory spectra for certain moduli spaces of Higgs bundles (in type A).
Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.