Title: A new proof of the Plancherel formula in the adelic setting

Speaker: Keith Ouellette, UCLA

Abstract:
Analogs of the classical Fourier transform, Plancherel formula, and Fourier inversion formula exist in the theory of automorphic forms on reductive adelic groups. In the first half of the talk, I will explain the Fourier theory for automorphic forms in the classical modular group case. In the second half, I will prove the Fourier inversion and Plancherel formulae for general reductive groups.