09:00 to 10:00 
Ehud De Shalit (The Hebrew University of Jerusalem, Israel) 
Moduli of pdivisible groups (Lecture 4) pdivisible groups and their moduli spaces play a prominent role in padic Hodge theory and in the study of Shimura varieties. Recent work of Scholze, Weinstein, Fargues and Fontaine has changed our perspective on them and yielded new results as well as new proofs of old theorems. This minicourse will be an introduction to moduli of pdivisible groups, starting with basics of Dieudonne' theory and ending with a sketch of Faltings' theorem on the isomorphism between the LubinTate tower and the Drinfel'd tower at the infinite level.



10:00 to 10:30 
 
Tea Break 


10:30 to 11:30 
Kiran Kedlaya (University of California San Diago, USA) 
Perfectoid spaces (Lecture 4) In this course, we will introduce perfectoid spaces, various examples, and the tilting equivalence. Additional topics will be treated as time permits.



11:45 to 12:45 
Denis Benois (University of Bordeaux, France) 
Introduction to padic Hodge theory (Lecture 4) In the first part of this course we review the classification of padic representations in terms of different rings of padic periods. In the second part, we define the curve of FontaineFargues $X^{FF}$ and overview the theory of vector bundles on $X^{FF}$ with applications to padic representations.



13:00 to 14:00 
 
Lunch 


14:00 to 15:00 
Arnab Saha (IIT Gandhinagar, India) 
Introduction to Witt vectors, deltarings, and prisms (Lecture 1) We will first give a development of the theory of Witt vectors from the point of view of deltarings, following Joyal. This is not the traditional approach, but it has the advantages of being more direct and not needing any mysterious formulas or arguments with padic congruences. In the later lectures, we will talk about the theory of prisms, as recently introduced by BhattScholze, which are certain kinds of deltarings.



15:15 to 16:15 
Rajneesh Singh (RMVU, India) 
Local Shtukas and Divisible Local Anderson Modules I will talk about the development of the analogue of crystalline Dieudonne theory for pdivisible groups in the arithmetic of function fields. In our theory, pdivisible groups are replaced by divisible local Anderson modules, and Dieudonné modules are replaced by local shtukas. We show that the categories of divisible local Anderson modules and of effective local shtukas are antiequivalent over arbitrary base schemes.



16:15 to 16:30 
 
Tea Break 


16:30 to 17:30 
Debargha Banerjee (IISERP, India) 
padic automorphic forms in the sense of Scholze (Lecture 2) In this course, we will introduce padic automorphic forms in the sense of Scholze. Completed cohomology, canonical and anticanonical subgroups will be introduced. We will study how to consider anticanonical subgroups in a tower. If time permits, we will study Galois representations using above.


