Regular Time: 13:00-14:30 & 15:00-16:30    23/11, 30/11, 7/12,  21/12

Time: 12:45-14:15 & 14:30-16:00    14/12

This short course aims to give an introduction to some recent progress on mod p Langlands program and mod p Jacquet-Langlands program. We will mainly focus on the case of GL_2(Q_p).
 We will discuss the following topics:
 (i)  Mod p representation theory of GL_2(Qp) and of quaternion algebra over Qp;
(ii)  Serre weights in the quaternion algebra setting;
(iii)  Galois deformation theory;
(iv)  Gelfand-Kirillov dimension of admissible representations of p-adic groups;
(v)   Scholze’s functor and some vanishing result.
Prerequisite:
Basic representation theory of p-adic groups; basic facts on local fields and p-adic analytic groups.  
References:
1.  C. Breuil, Representations of Galois and of GL_2 in characteristic p, course at Columbia University.   
2.  C. Cheng, Mod p representations of local division algebras over p-adic fields, unpublished notes.
3.  C. Khare, A local analysis of congruences in the (p,p) case. II, Invent. Math. 143 (2001), 129-155.
4.  P. Scholze, On the p-adic cohomology of the Lubin-Tate tower, Ann. Sci. ENS, 51 (2018), 811-863.
5.  V. Paskunas, On the Breuil-Mezard conjecture, Duke Math. J. 164 (2015), 297-359.
6.  V. Paskunas, On some consequences of a theorem of Ludwig, arXiv: 1804.07567