Title: Local character expansions, hyperelliptic curves, and endoscopy
Speaker: Cheng-Chiang Tsai
Speaker Info: Harvard
Brief Description:
Special Note:
Abstract:
A representation of a reductive p-adic group has its character as a distribution on the group, invariant under conjugation. The asymptotic behavior of the character is given by Harish-Chandra's local character expansion, which expressed the character near the identity as a finite-term expansion (which is a linear combination of Fourier transforms of nilpotent orbital integrals). In this talk, we show via example how the coefficients in this expansion may arise as the numbers of rational points on varieties over the residue field, which will be numbers of rational points on certain covers of hyperelliptic curves in our example. We'll also talk about how the phenomenon of endoscopy appears as geometric identities regarding H^1 of these curves.Date: Monday, November 24, 2014