Time：14:00-16:00, Wednesday, December 17 2025
Venue：E14-212
Speaker：Fangyang Tian, Zhejiang University
Title：The Philosophy of Cusp Forms for Real Symmetric Spaces
Abstract: One of the most fundamental problems in representation theory is to understand the building blocks of representations. For reductive groups over local fields of characteristic zero, such building blocks are supercuspidal representations in the non-archimedean case; discrete series in the archimedean case. A natural question is to ask a similar question for a symmetric spaces G/H.
In this talk, I will explain how Harish-Chandra's philosophy of 'cusp forms' is generalized to the case of symmetric spaces through the years; some successful examples typically for rank one case due to E. van den Ban, J. Kuit; and what techinical difficulties that one will face for marching to higher rank case. Along the talk, I will also explain the theory with an example computed by myself and my student Y. Yao. Most of the talk are suitable for non-experts, and hence graduate students are most welcome.
