Yihang Zhu ( Harvard)
The Hasse-Weil zeta functions of the intersection cohomology of minimally compactified orthogonal Shimura varieties

Abstract: 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. The strategy proposed by Langlands was to compare the Grothendieck-Lefschetz trace formula for Shimura varieties with the trace formula for automorphic forms, which was later made more precise by Kottwitz. Recent progress in various aspects of the field has allowed the extension of the program to some Shimura varieties not treated before. In the particular case of orthogonal Shimura varieties, we discuss the proof of Kottwitz's conjectural comparison (between the intersection cohomology of their minimal compactifications and the stable trace formulas). Key ingredients include point-counting on abelian type Shimura varieties, a comparison between Harish Chandra characters and Kostant's Theorem on unipotent Lie algebra cohomology, and a comparison between different normalizations of the transfer factors for real endoscopy to get all the signs right. br>