Geometric Methods in Rep Theory Seminar – Jayce Getz (Duke)

On the Poisson summation conjecture

Abstract: Braverman, Kazhdan, Lafforgue, Ngo, and Sakellaridis have conjectured that Fourier analysis on a vector space is but the first example of a larger phenomenon. More generally, one should have Schwartz spaces, Fourier transforms, and, crucially, Poisson summation formulae for affine spherical varieties. I will give an account of the few cases in which the conjecture is known, and describe some techniques for proving new cases from old cases.

Geometric Methods in Representation Theory Seminar