# Mathematical Sciences Research Institute

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# Seminar

NGM Pizza Seminar: Hyperelliptic curves, local character expansions, and endoscopy November 14, 2014 (11:00 AM PST - 11:45 AM PST)
Parent Program: New Geometric Methods in Number Theory and Automorphic Forms MSRI: Simons Auditorium
Speaker(s) Cheng-Chiang Tsai (Stanford University)
Description No Description
Video
A representation of a reductive p-adic group has its character as a distribution on the group. Its asymptotic behavior near the identity is given by a finite-term local character expansion of Harish-Chandra. In this talk, we state a result giving a few terms in the local character expansions for certain supercuspidal representations of a ramified unitary group. The numbers are related to the number of rational points on certain covers of hyperelliptic curves. We'll then talk about how endoscopy transfer for these characters is related to geometric identities regarding H^1 of these curves. A side goal will be to demonstrate possible similarity between such phenomenon and the work of Bhargava-Gross on arithmetic invariant theory of $SO_{2n+1}$ on $\text{Sym}^2$.