# Arithmetic Electric-Magnetic Duality

PIRSA ID:
24020062

Series:
Colloquium

Event Type:
Seminar

Scientific Area(s):

Other

End date:

Speaker(s):

- David Ben-Zvi, The University of Texas at Austin

The Langlands program is a grand organizing vision for a large slice of number theory and representation theory. A shockingly accurate metaphor for the Langlands program has emerged as electric-magnetic duality in four-dimensional gauge theory, but where the role of spacetime is played by objects from arithmetic. I will describe recent work with Yiannis Sakellaridis and Akshay Venkatesh, in which we apply ideas from QFT (the Gaiotto-Witten electric-magnetic duality for boundary theories) to a fundamental problem in number theory, predicting the relation between L-functions of Galois representations and integrals of automorphic forms.

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