# Workshop on Galois Representations and Automorphic Forms

The workshop combined background talks aimed at graduate students and post-docs with research reports on the latest developments. The workshop concentrated on the following topics:

Automorphy and potential automorphy of Galois representations and applications.

Integral models of cohomology of Shimura varieties and Rapoport-Zink spaces.

p-adic comparison theorems and applications to modular/automorphic forms.

p-adic L-functions and main conjectures, especially methods coming from automorphic forms.

The p-adic Langlands program.

## Organizers:

Pierre Colmez, National Center for Scientific Research/IAS, Michael Harris, University of Paris VII/IAS, Christopher Skinner, Princeton University/IAS, Richard Taylor, Harvard University/IAS

## Speakers:

D. Burns (King's College London), F. Calegari (IAS), Ana Caraiani (Harvard), L. Clozel (U Paris), G. Dospinescu (Ecole Polytechnique), T. Gee (IAS), D. Geraghty (IAS), M. Emerton (Northwestern), H. Hida (UCLA), A. Iovita (Concordia), M. Kakde (Univ College London), T. Kaletha (IAS), S. Morel (IAS), V. Paskunas (Univ Bielefeld), V. Pilloni (Columbia), P. Scholze (Univ Bonn), M-F. Vigneras (Univ Jussieu) and J. Weinstein (IAS)

## Participants:

The following people were in attendance for most, if not all, of the workshop activities: L. Berger, F. Diamond, T. Haines, M. Harris, F. Herzig, C. Khare, K.-W. Lan, T. Liu, E. Mantovan, J. Newton, S. W. Shin, C. Skinner, J. Suh, R. Taylor, Y. Tian, E. Urban, A. Wiles.

Video lectures are here: https://www.ias.edu/video/graf

Agenda

## All talks took place in Simonyi Hall Seminar Room

Monday, March 21, 2011

10:00 - 11:00 Laurent Clozel, The proof of the Burger-Sarnak conjecture

11:30 - 12:30 Tasho Kaletha, Supercuspidal L-packets

12:30 - 2:15 Lunch (IAS Dining Hall)

2:30 - 3:30 Vincent Pilloni, Construction of eigenvarieties and coherent cohomology

3:30 - 4:00 Tea (Fuld Hall Common Room)

4:00 - 5:00 Adrian Iovita, An overconvergent Eichler-Shimura map

Tuesday, March 22, 2011

10:00 - 11:00 Ana Caraiani, Local-global compatibility and monodromy

11:30 - 12:30 Sophie Morel, Intersection cohomology is useless

12:30 - 2:15 Lunch (IAS Dining Hall)

2:30 - 3:30 Peter Scholze, Perfectoid spaces

3:30 - 4:00 Tea (Fuld Hall Common Room)

4:00 - 5:00 Jared Weinstein, A semistable model for the tower of modular curves

Wednesday, March 23, 2011

10:00 - 11:00 Frank Calegari, Minimal modularity lifting theorems for imaginary quadratic fields.

11:30 - 12:30 Matthew Emerton, p-adic Hodge-theoretic properties of etale cohomology with mod p coefficients, and the cohomology of Shimura varieties - 1

12:30 - 2:15 Lunch (IAS Dining Hall)

2:30 - 3:30 Toby Gee, p-adic Hodge-theoretic properties of etale cohomology with mod p coefficients, and the cohomology of Shimura varieties - 2

3:30 - 4:00 Tea (Fuld Hall Common Room)

4:00 - 5:00 David Geraghty, Local-global compatibility at primes dividing l

Thursday, March 24, 2011

10:00 - 11:00 Marie-France Vigneras, From general etale (phi, Gamma)-modules to representations of G(Q_p)

11:30 - 12:30 Vytautas Paskunas, The image of Colmez's Montreal functor

12:30 - 2:15 Lunch (IAS Dining Hall)

2:30 - 3:30 Gabriel Dospinescu, Locally algebraic vectors in the p-adic Langlands correspondence

3:30 - 4:00 Tea (Fuld Hall Common Room)

Friday, March 25, 2011

10:00 - 11:00 Haruzo Hida, Vanishing of the $\mu$-invariant of $p$-adic Hecke $L$ functions

11:30 - 12:30 David Burns, Recent developments in non-commutative Iwasawa theory - 1

12:30 - 2:15 Lunch (IAS Dining Hall)

2:30 - 3:30 Mahesh Kakde, Recent developments in non-commutative Iwasawa theory - 2

~Finish