Joint IAS/Princeton University Number Theory Seminar

The Hasse-Weil zeta functions of the intersection cohomology of minimally compactified orthogonal Shimura varieties

Initiated by Langlands, the problem of computing the Hasse-Weil zeta functions of Shimura varieties in terms of automorphic L-functions has received continual study. We will discuss how recent progress in various aspects of the field has allowed the extension of the project to some Shimura varieties not treated before. In the particular case of orthogonal Shimura varieties, we discuss the computation of the Frobenius-Hecke traces on the intersection cohomology of their minimal compactifications, and the comparison to the Arthur-Selberg trace formula via the process of stabilization. Key ingredients include comparing Harish Chandra character formulas to Kostant's Theorem on Lie algebra cohomology, and a comparison between different normalizations of the transfer factors for real endoscopy to get all the signs right.

Date & Time

October 20, 2016 | 4:30pm – 5:30pm

Location

S-101

Speakers

Yihang Zhu

Affiliation

Harvard University

Event Series

Categories