Last updated:   April 29, 2019.

Geometrization of the local Langlands program
Key note speaker: Jared Weinstein (Boston University)
Supported by the Centre de Recherches Mathématiques, Montréal.

McGill University, Monday, May 6 - Friday, May 10, 2019
Organizers: Eyal Goren and Henri Darmon (McGill)


Short description: The Langlands program links automorphic forms and Galois representations (of a local or global field).  In contrast, the geometric Langlands program takes a curve X over the complex numbers, and links the moduli space of vector bundles on X to local systems on X. There is a tidy analogy between the two programs, but generally, researchers in the two programs do not interact.  
    A beautiful program initiated by Fargues reveals the unity of the two programs over the field of p-adic numbers.  In this program, the role of X is played by the Fargues-Fontaine curve.  The goal of this meeting is to master the tools required to understand Fargues' suite of conjectures.


Please note the following:


Program

Monday 09:45   Registration and welcome
10:00 - 12:00   Jared Weinstein:
"Classical geometric Langlands
  - Automorphic forms versus automorphic sheaves
  - The Satake equivalence
  - Statement of the conjecture"
14:30 - 16:30   David Hansen:
"Lightning review of p-adic geometry"

Coffee break
Tuesday 10:00 - 12:00   Jared Weinstein:
"The Fargues-Fontaine curve
 - Construction, basic properties
 - Classification of vector bundles
 - Relation to p-divisible groups"
14:30 - 16:30   David Hansen:
"Fun with vector bundles on the Fargues-Fontaine curve"

Coffee break
Wednesday 10:00 - 12:00   Jared Weinstein:
"The stack Bun_G
 - Kottwitz' set B(G)
 - Sketch of the uniformization
 - Hecke operators
 - Local Shimura varieties"
14:30 - 16:30   Arthur-César Le Bras:
"Local class field theory and the Fargues-Fontaine curve"

Coffee break
Thursday 10:00 - 12:00   Jared Weinstein:
"The conjectures
 - Local Langlands
 - Fargues' sheaf
 - The eigencategory"
14:30 - 16:30   Sophie Morel
"Drinfeld's proof of the global Langlands correspondence for GL(2)"

Coffee break

17:00 - 18:00    Laurent Fargues:
 "Where does the conjecture come from? What happened in Orsay, Trieste and Berkeley?" Part I
Friday


10:00 - 12:00   Laurent Fargues:
  "Where does the conjecture come from? What happened in Orsay, Trieste and Berkeley?" Part II
13:30 - 15:30   Jared Weinstein:
"What's known:
 - The case of a torus
 - The automorphic-to-Galois construction of Fargues-Scholze"

Coffee break


Participants

1
Rebecca Bellovin
Annie Carter
Antonio Cauchi
2
William Yun Chen
Henri Darmon
Maria Ines de Frutos Fernandez
3
Ehud de Shalit
Jordan Ellenberg
Payman Eskandari
4
Laurent Fargues
Tony Feng
Michele Fornea
5
Ildar Gaisin
Toby Gee
Eyal Goren
6
Andrew Granville
David Hansen
Florian Herzig
7
Serin Hong
Benjamin Howard
Alexander Ivanov
8
Tasho Kaletha
Erick Knight
Karol Koziol
9
Stephen Kudla
Arthur-César Le Bras
Daniel Le
10
Antonio Lei
Qirui Li
David Lilienfeldt
11
Michael Lipnowski
Zheng Liu
Jacob Lurie
12
Reginald Lybbert
Richard Magner
Matteo Tammiozo
13
Sophie Morel Isabella Negrini Corentin Perret-Gentil
14
Alice Pozzi
Giovanni Rosso
Vinayak Vatsal
15
Guhan Venkat
Jan Vonk
Haining Wang
16
Torsten Wedhorn
Peter Xu
Zijian Yao
17
Lynnelle Ye




Location of the conference:
All lectures and coffee breaks take place in Burnside Hall, McGill university. The official address of the building is 805 Sherbrooke street West. In practice, get to the intersection of the streets "Sherbrooke" and "McGill college" and stand facing the campus. Burnside hall will be at 2 o'clock. It is a tall ugly concrete building.

Lectures will take place in room 1104. Take the elevators to the 11th floor and as you exit turn left and then right to find the door to the room. There is study space and small conference rooms adjacent to the lecture room that you may use when you wish.

Coffee breaks are in the afternoon after the talk and will be offered in the lounge on the 10th floor. The lounge is "behind" the elevators.

Restaurant recommendations: some possible places for lunch


Hotel recommendations:
The conference is held at McGill, which is right in the center of downtown (corner of Sherbrooke street and McGill College street). Basically any hotel in the vicinity will do. We often use Hotel Ambrose (basic, more on budget hotel), Hotel Meridien Versailles, Residence Inn by Marriott on Peel street, and Appartements Trylon (studio apartments). But, honestly, an AIRBNB might be the best option and even more affordable if shared.