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On discrete series conjecture and unfolding

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Fei Chen

时间

2025年09月29日 10:00 至 11:00

地点

Shuangqing-B627

摘要

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.