GAAG seminar - The Langlands formula and perverse sheaves

We start by introducing a formula of Gindikin-Karpelevich that expresses the constant term of an Eisenstein series as a product of Gamma functions, which is later reinterpreted by Langlands using Satake isomorphism in his famous work of Euler products. This formula reflects a phenomenon of "wall-crossing" that occurs in many situations that concern parabolic induction/restriction. I will introduce a joint work with M.Kapranov, V. Schechtman and O.Schiffmann in which for a reductive group G, we construct a so-called Perverse Coxeter category that encodes behavior of parabolic induction/restriction and relate it with the perverse sheaves on the configuration space h/W. If time permits, we will discuss the relation of our category with operads and some interpretation in geometric Langlands program.