The purpose of this semester-long seminar is to go over the theory of continuous and locally analytic representations of p-adic groups. The first half will focus on the theory of Schneider-Teitelbaum, following their Hangzhou note. The second half may learn Orlik-Strauch representations and some results of Arkedov.
(3/1) Yiwen Ding: Introduction: give a quick introduction to p-adic local Langlands program and motivate the study of continuous and locally analytic representations. (video, notes)
(3/8) Xiaozheng Han: Following [1, § 1-5]: basic facts on locally convex topological space, in particular p-adic Banach space and Fréchet space. Explain and prove the open mapping theorem (cf. [2]). (video, notes)
(3/15) Cong Zhang: Following [1, § 6-8]: space of compact type, dual space, prove Banach-Stainhaus (I). (video1, video2, notes)
(3/22) Cong Zhang: Following [1, § 6-8]: space of compact type, dual space, prove Banach-Stainhaus (II). (video1, video2, notes)
(3/29) Yiqin He: Following [1, § 9-11]: continuous and locally analytic functions, distributions. (video1, video2, notes)
(4/5) National Qing Ming Holiday.
(4/12) Jiawei An: Following [1, § 12] [4]: distribution algebras, discuss the case for p-adic-integers in details (Amice transform etc.).
(4/19) Benchao Su: Following [1, § 14-17]: continuous and locally analytic representations.