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

## February 23 @ 4:00 pm - 5:00 pm

**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.