You are cordially invited to the seminars organized by the Department of Mathematics.
Speaker: Pam Gu (University of Michigan)
“An introduction to Poisson summation conjecture”
Abstract: The Poisson summation formula identifies the sum of a function over the
integers to the sum of its Fourier transform over the integers. In 1972, generalizing Tate’s
thesis, Godement and Jacquet used the Poisson Summation formula to prove the functional equation and analytic continuation of automorphic L-functions for GLn (functions with similar properties to the Riemann zeta function). Generalizing Godement-Jacquet’s theory, conjectures of Braverman-Kazhdan, Lafforgue, Ngˆo and Sakellaridis suggest that every affine spherical variety (a geometric object equipped with certain group action) admits a generalized Poisson summation formula. We refer to this conjecture as the Poisson summation conjecture. The Poisson summation conjecture implies the functional equation and meromorphic continuation for fairly general automorphic L-functions, which by the converse theorem, implies Langlands functoriality in great generality. In this talk, I will give a gentle introduction to this circle of ideas, and then talk about some of my current and future research related to this conjecture and its application to L-functions.
Date: April 2, Thursday
Time: 19:00 (Ankara)
Place: Zoom
To request the event link, please send a message to gokhan.yildirim@bilkent.edu.tr