Session S21 - Galois representations and automorphic forms

Wednesday, July 21, 19:20 ~ 20:00 UTC-3

Harmonic analysis on certain spherical varieties

Jayce Getz

Duke University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Braverman and Kazhdan proposed a conjecture, later refined by Ngo and partially set in the framework of spherical varieties by Sakellaridis, that asserts that affine spherical varieties admit Schwartz spaces, Fourier transforms, and Poisson summation formulae. If proven, the conjecture would imply Langlands functoriality in great generality. In this talk I will describe explicit formulae for the Fourier transform on Braverman-Kazhdan spaces (also known as pre-flag varieties) and for certain spherical varieties that are built out of triples of quadratic spaces.

Joint work with Chun-Hsien Hsu (Duke University) and Spencer Leslie (Duke University).

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