# Arithmetic Electric-Magnetic Duality

### APA

Ben-Zvi, D. (2024). Arithmetic Electric-Magnetic Duality. Perimeter Institute. https://pirsa.org/24020062

### MLA

Ben-Zvi, David. Arithmetic Electric-Magnetic Duality. Perimeter Institute, Feb. 15, 2024, https://pirsa.org/24020062

### BibTex

@misc{ pirsa_PIRSA:24020062, doi = {10.48660/24020062}, url = {https://pirsa.org/24020062}, author = {Ben-Zvi, David}, keywords = {Other}, language = {en}, title = {Arithmetic Electric-Magnetic Duality}, publisher = {Perimeter Institute}, year = {2024}, month = {feb}, note = {PIRSA:24020062 see, \url{https://pirsa.org}} }

David Ben-Zvi The University of Texas at Austin

## Abstract

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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