Periods, L-functions, and duality of Hamiltonian spaces

Abstract: The relationship between periods of automorphic forms and L-functions has been studied since the times of Riemann, but remains mysterious. In this talk, I will explain how periods and L-functions arise as quantizations of certain Hamiltonian spaces, and will propose a conjectural duality between certain Hamiltonian spaces for a group $G$, and its Langlands dual group $\check G$, in the context of the geometric Langlands program, recovering known and conjectural instances of the aforementioned relationship. This is joint work with David Ben-Zvi and Akshay Venkatesh.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

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MIT number theory seminar

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