Spherical varieties, L-functions, and crystal bases

Jonathan Wang (MIT Mathematics)

23-Sep-2020, 20:30-21:30 (4 years ago)

Abstract: The program of Sakellaridis and Venkatesh proposes a unified framework to study integral representations of L-functions through the lens of spherical varieties. For X an affine spherical variety, the (hypothetical) IC complex of the infinite-dimensional formal arc space of X is conjecturally related to special values of local unramified L-functions. We formulate this relation precisely using a new conjectural geometric construction of the crystal basis of a finite-dimensional representation (determined by X) of the dual group. We prove these conjectures for a large class of spherical varieties. This is joint work with Yiannis Sakellaridis.

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.

Organizers: André Lee Dixon*, Ju-Lee Kim, Roman Bezrukavnikov*
*contact for this listing

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