Room 509, Cosmology Building, NTU
(臺灣大學次震宇宙館 509研討室)
The global and local Langlands-Kottwitz methods (1): Survey of current status
Yihang Zhu (Yau Mathematical Sciences Center, Tsinghua University)
Abstract
The Langlands-Kottwitz method seeks to express the trace of Frobenius-Hecke operators on the cohomology of Shimura varieties in a formula resembling the geometric side of the Arthur-Selberg trace formula. This formula involves, among other things, orbital and twisted orbital integrals, which are intriguing objects in local harmonic analysis. This project has been pursued by mathematicians for over 40 years.
In the first lecture, we will survey the current status of Langlands-Kottwitz methods on the trace formula for Frobenius-Hecke operators on the cohomology of Shimura varieties.
References:
R. Kottwitz, Shimura varieties and lambda-adic representations (in vol.1 of the Ann Arbor proceedings, 1988)
M. Kisin, S. W. Shin, and Y. Zhu, The stable trace formula for Shimura varieties of abelian type
M. Rapoport, A guide to the reduction modulo p of Shimura varieties
X. Zhu, Tame categorical local Langlands correspondence
Organizer
Chia-Fu Yu(Academia Sinica)
