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Watch a mathematics lecture from Harvard CMSA where Duke University's Jayce Getz explores the Poisson summation conjecture and its applications in algebraic number theory. Delve into the conjecture proposed by Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis, which suggests that spherical varieties over global fields possess Schwartz spaces, Fourier transforms, and a generalized Poisson summation formula. Learn how new cases of the conjecture can be derived from known instances using the fiber bundle method, and discover an approach to proving the functional equation of triple product L-functions. The presentation includes collaborative work with Pam Gu, Chun-Hsien Hsu, and Spencer Leslie, offering advanced insights into this specialized area of mathematics.
