Thursday, March 23, 2023, 8:30am, 359 Gross Hall

Miao (Pam) Gu (Duke University, Mathematics)

- Conjectures of Braverman-Kazhdan, L. Lafforgue, Ngô and Sakellaridis imply that all affine spherical varieties admit generalized Poisson summation formula. In this dissertation we establish a generalized Poisson summation formula for certain spaces of test functions on the zero locus of a quadratic form. The functions are built from the Whittaker coefficients of automorphic representations on $\mathrm{GL}_n$. We also give an expression of the local factors where all the data are unramified.

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