BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar On discrete series conjecture and unfolding
On discrete series conjecture and unfolding
Organizers
Hansheng Diao , Heng Du , Yueke Hu , Bin Xu , Yihang Zhu
Speaker
Fei Chen
Time
Monday, September 29, 2025 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
Abstract
Let $X$ be a spherical variety defined over a p-adic field. One of the central problems in the relative Langlands program is to understand the Plancherel decomposition of $L^2(X)$. For a large class of spherical varieties, Sakellaridis-Vankatesh explicit this decomposition up to knowledge of discrete spectrums of boundary degenerations of $X$ under the assumption that their discrete series conjecture holds. Sakellaridis-Vankatesh also propose a construction called unfolding and conjecture this construction would solve their discrete series conjecture. In this talk, we will discuss relevant backgrounds and report our progress toward this direction.