PIRSA:24020062 Scientific Series Other

DOI10.48660/24020062

Series: Colloquium

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

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

@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}}
}

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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