2022-10-28 Introduction, motivation, and organization (Jiacheng)

2022-11-4 Complex uniformization and Tate's uniformization of elliptic curves (Tam)

2022-11-11 Tate algebras (suggestion: we should cover the Weierstraß Preparation Theorem) (Mohammadreza)

2022-11-18 Affinoid algebras and affinoid spaces (general theory) (Cédric)

2022-11-25 Example: the projective line (suggestion: Chapter 2 in Fresnel and van der Put's book and we should see Grothendieck topologies in this concrete case first) (Katharina)

2022-12-2 Grothendieck topologies, rigid analytic spaces and rigid analytification (general theory) (Mihir)

2022-12-9 Example: generic fibre of Drinfeld's upper half plane (suggestion: first construct this as a subset of the rigid analytic projective line, and then show that this defines a rigid analytic variety) (Shilun)

2023-2-3 Example: special fibre of Drinfeld's upper half plane (equivalent ways of defining the p-adic Bruhat--Tits tree) (Luochen)

2023-2-17 p-adic Schottky groups and Mumford's uniformization (suggestion: find some concrete examples) (Shilun)

2023-3-3 Arithmetic of Shimura curves (Luochen)

2023-3-10 p-adic uniformization of Shimura curves (Cerednik-Drinfeld theorem, suggestion: the key step is to consider certain supergroups of Schottky groups containing elements of finite order) (Jiacheng)

Optional

1. Raynaud's proof of Abhyankar's Conjecture for the affine line in positive characteristic (following Week 3)

2. Formal geometry and formal schemes; Raynaud's view on rigid analytic geometry

3. (A sketch of) Drinfeld's proof of the main theorem

4. Application: cohomology of rigid analytic spaces

5. Fundamental domains of p-adic Schottky groups