Speaker: Raphaël Beuzart-Plessis (Marseille)

Title: On the formal degree conjecture for classical groups

Abstract: A conjecture of Hiraga, Ichino and Ikeda expresses the formal degree of a discrete series of a (algebraic) reductive group over a local field in terms of the adjoint gamma factor of its Langlands parameter. It can be checked for real reductive groups using work of Harish Chandra and the explicit form of the Langlands correspondence in this case. For classical groups over a p-adic field, the conjecture was established for odd orthogonal groups as well as unitary groups by two completely different methods. In this talk, I will explain a proof for symplectic and even orthogonal p-adic groups based on properties of twisted endoscopy and ideas originating from Shahidi relating residue of intertwining operators to twisted orbital integrals. This method can actually be readily adapted to treat odd orthogonal and unitary groups as well.