时间： 4月25日（周一）下午 14:00—15:30
4月27日（周三）下午 14:00—15:30
4月29日（周五）下午 14:00—15:30

摘要：
Lecture 1: Survey on some notions of integral p-adic Hodge theory
We firstly quickly review the notion of crystalline representations and Fontaine modules. We will then survey several ``linear algebra" categories in integral p-adic Hodge theory, including Fontaine-Laffaille modules, strongly divisible modules, Kisin modules, and (phi, \hat G)-modules. We will try to give some examples, without any proofs.

Lecture 2: Kisin modules, and some applications
We will try to give a sketch of the proof of existence of Kisin modules. We then present some applications of Kisin modules, in particular, its relation with p-divisible groups. If time permits, we also discuss its relation with Galois deformation rings.

Lecture 3: Kisin modules and local models
We will present the work of Caraiani-Levin, which shows that the moduli of Kisin modules with descent data naturally have the structure of local models. If time permits, we will discuss its application to Serre weight conjectures.