Tsao-Hsien Chen, Minnesota

Bernstein centers of p-adic groups and perverse sheaves

I will explain a description of the  Bernstein center of a split p-adic reductive group as a limit of parahoric Hecke algebras, extending the previous work of Bezrukavnikov-Kazhdan-Varshavsky on explicit descriptions of depth-r Bernstein projectors. Then I will explain how such a  description allows us to apply the theory of perverse sheaves (e.g. character sheaves on reductive groups, graded Lie algebras, parahorics or Gaitsgory's central sheaves) to study  Bernstein centers. I will discuss some examples and applications, including a decomposition of the category of smooth representations into a product of full subcategories indexed by restricted depth-r Langlands parameters. Time permitting, I will mention connections with Stable Center Conjecture in Local Langlands correspondence.

The talk is based on joint works with Sarbartha Bhattacharya, Charlotte Chan, Stephen Debacker and Cheng Chiang Tsai.

Joakim Faergeman, Yale

Motivic realization of rigid local systems on curves via geometric Langlands

A natural problem in the study of local systems on complex varieties is to characterize those that arise in a family of varieties. We refer to such local systems as motivic. Simpson conjectured that for a reductive group G, rigid G-local systems with suitable conditions at infinity are motivic. This was proven for curves when G = GL_n by Katz who classified such rigid local systems. In this talk, we prove Simpson's conjecture for curves for an arbitrary reductive group G. Our proof goes through the (tamely ramified)  geometric Langlands program in characteristic zero. If time permits, we state a generalization of Simpson's conjecture to an arbitrary smooth projective variety.

Sanath Devalapurkar, Chicago

TBD

TBD

Pam Gu, Michigan

TBD

TBD