# CMSA Colloquium: Electric-Magnetic Duality for Periods and L-functions

CMSA EVENTS

##### Speaker:

David Ben-Zvi *- U Texas*

I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.

A fundamental aspect of the Langlands correspondence -- the relative Langlands program -- studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don't seem to line up.

We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the *relative *Langlands program as duality in the presence of supersymmetric boundary conditions. As a result, the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

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Zoom: https://harvard.zoom.us/j/95505022117