Title: Langlands duality and categorical traces
Speaker: Nick Rozenblyum
Speaker Info: University of Chicago
Brief Description: Virtual (Zoom) Talk
Meeting ID: 997 6959 0131Date: Thursday, March 04, 2021
Meeting Password: First word of the name of the seminar (in small letters)
Abstract: By analogy with characteristic p geometry, Beilinson and Drinfeld formulated a categorical analogue of the Langlands program for Riemann surfaces over the complex numbers. One of the remarkable features of this conjecture is its relation to conformal field theory and higher dimensional quantum field theory. However, this formulation is very specific to complex algebraic geometry. I will describe a general categorical conjecture suitable to arbitrary geometric settings, including l-adic sheaves on algebraic curves over finite fields. One remarkable application of these ideas is a description of the space of automorphic forms as the categorical trace (aka Hochschild homology) of Frobenius. This is joint work with Arinkin, Gaitsgory, Kazhdan, Raskin, and Varshavsky.