Abstract: Emerton and Zhu have proposed a conjectural formula for compactly supported cohomology of Shimura varieties in terms of categorical local Langlands. In this case the contribution at infinity comes from the Shimura datum. I will discuss how one can interpret the archimedean contribution to cohomology of a general locally symmetric space in terms of categorical Vogan duality. This is joint work with Davis and Emerton. 

Introduction: Professor Kari Vilonen is a renowned mathematician. His research interest include representation theory and algebraic geometry. He has made fundamental contributions to the geometric Langlands program, representation theory of Lie groups and the theory of D-modules. He was an invited speaker at ICM 1998. He received the Humboldt Research Award (2014), Simons Fellowship (2014), Guggenheim Fellowship (1997), AMS Centennial Fellowship (1991).