Quantization and Duality for Spherical Varieties

Abstract: I will present joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which we apply a perspective from topological field theory to the relative Langlands program. To a spherical variety one can assign two quantization problems, automorphic and spectral, both resulting in structures borrowed from QFT. The automorphic quantization (or A-side) organizes objects such as periods, Plancherel measure, theta series and relative trace formula, while the spectral quantization (or B-side) organizes L-functions and Langlands parameters. Our conjectures describe a duality operation on spherical varieties, which exchanges automorphic and spectral quantizations (and may be seen as Langlands duality for boundary conditions in 4d TFT, a refined form of symplectic duality / 3d mirror symmetry).

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.