Spectral decomposition in geometric Langlands
Nick Rozenblyum (Chicago)
Title: Spectral decomposition in geometric Langlands
Abstract: We will describe a version of spectral decomposition in the setting of geometric Langlands. Specifically, we will explain how a version of higher categorical trace applied to the category of representations of the Langlands dual group gives an action on the automorphic category of the category of quasi-coherent sheaves on the moduli space of local systems. We will introduce the trace conjecture (to be discussed in Gaitsgory's talk) which gives, upon additionally taking the categorical trace of Frobenius, V. Lafforgue's spectral decomposition of the space of automorphic forms as well as expected structures on the cohomologies of shtukas, which give rise to a localization of the space of automorphic forms on the moduli space of arithmetic local systems. This is joint work with Arinkin, Gaitsgory, Kazhdan, Raskin, and Varshavsky.
Recording taken from the Arithmetic Geometry and Quantum Field Theory seminar, organised by Jeff Harvey and Minhyong Kim