BIMSA-YMSC Tsinghua Number Theory Seminar
Organizers：
Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu
Speakers：
Yu Fu (Caltech)
Emile Okada (NUS)
Time：
Monday, 10:00-12:00
Dec. 30 2024
Venue：
C654, Shuangqing Complex Building A
Title & Abstract：
Yu Fu (Caltech)
Title: The p-adic analog of the Hecke orbit conjecture and density theorems toward the p-adic monodromy
Abstract: The Hecke orbit conjecture predicts that Hecke symmetries characterize the central foliation on Shimura varieties over an algebraically closed field k of characteristic p. The conjecture predicts that on the mod p reduction of a Shimura variety, any prime-to-p Hecke orbit is dense in the central leaf containing it, and was recently proved by a series of nice papers.
However, the behavior of Hecke correspondences induced by isogenies between abelian varieties in characteristic p and p-adically is significantly different from the behavior in characteristic zero and under the topology induced by Archimedean valuations. In this talk, we will formulate a p-adic analog of the Hecke orbit conjecture and investigate the p-adic monodromy of p-adic Galois representations attached to points of Shimura varieties of Hodge type. We prove a density theorem for the locus of formal neighborhood associated to the mod p points of the Shimura variety whose monodromy is large and use it to deduce the non-where density of Hecke orbits under certain circumstances.
Emile Okada (NUS)
Title: Involutivity in the unramified local Langlands correspondence
Abstract: In 1995 Lusztig gave a local Langlands correspondence for unramified representations of inner-to-split adjoint groups combining many deep results from type theory and geometric representation theory. In this talk I will present an equivariant reformulation of his construction revealing interesting new structures, and with a view toward proving functoriality results in this framework. I will pay special attention to functoriality results for the contragredient and Aubert duality which are important involutions on the set irreducible smooth representations.
