Last updated:   March 7, 2019.

Geometrization of the local Langlands program

Monday, May 6 - Friday, May 10, 2019

Key note speaker: Jared Weinstein (Boston University)

Organizers: Eyal Goren and Henri Darmon (McGill)

Lectures begin on the morning of May 6 and finish on the afternoon of May 10.

Due to limited space, participation is by invitation only.

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.

The general structure of the program is 4 hours per day, with morning lectures delivered by Jared and afternoon lectures delivered by participants of the workshop. Lectures will start the morning of May 6 and end in the afternoon of May 10. It is therefore advisable for participants to be in Montreal on May 5 or before and depart either during the night of the May 10, or later.


This webpage will be update as more information becomes available.


Program

Monday
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
Tuesday
10:00 - 12:00   Jared
The Fargues-Fontaine curve
 - Construction, basic properties
 - Classification of vector bundles
 - Relation to p-divisible groups
14:30 - 16:30   David Hansen
Wednesday
10:00 - 12:00   Jared
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
Thursday
10:00 - 12:00   Jared
The conjectures
 - Local Langlands
 - Fargues' sheaf
 - The eigencategory
14:30 - 16:30   Sophie Morel
Friday
10:00 - 12:00   Laurent Fargues

13:30 - 15:30   Jared
What's known
 - The case of a torus
 - The automorphic-to-Galois construction of Fargues-Scholze

List of possible topics for the afternoon talks:
- A primer on p-adic geometry
- Vector bundles on the Fargues-Fontaine curve
- A discussion of Drinfeld's work on geometric Langlands
- A discussion of local Langlands over a p-adic field
- V. Lafforgue's work on function fields


Background literature:





Participants

1
Laurent Fargues
David Hansen
Arthur-César Le Bras
2
Sean Howe*
Eric Knight
Rebecca Bellovin
3
Serin Hong
Ricky Magner
Tony Feng
4
Zijian Yao
Lynnelle Ye
Maria Fernandez
5
Mike Lipnowksi
Eyal Goren
Henri Darmon
6
Nike Vatsal
Jan Vonk
Andrew Granville
7
Ehud De Shalit
Steve Kudla
Giovanni Rosso
8
Sophie Morel
Alice Pozzi
Isabella Negrini
9
Massimo Bertolini*
Jordan Ellenberg*
Jacob Lurie
10
Karol Koziol
Tasho Kaletha
Annie Carter
11
Florian Herzig
Toby Gee
Qirui Li
12
Daniel Le
Ben Howard
Tosten Wedhorn
13
Kartik Prasanna*
Luis Garcia
Peter Xu
14
William Chen
Zheng Liu
Haining Wan
15
David Lilianfeldt
Alexander Ivanov
Corentin Perret-Gentil
16
Michele Fornea
Reginald Lybbert
Antonio Lei
*=with high probability



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.