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)

Notes (courtesy of Tony Feng and the speakers): here

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:

• Lectures begin on the morning of May 6 and finish on the afternoon of May 10.
  
• All lectures take place at McGill University, Burnside Hall, 805 Sherbrooke Street West, Room 1104.
• The discussion rooms and study area adjacent to the lecture room are available for the use of participants at all times.
• The coffee breaks take place in the Lounge on the 10th floor, behind the elevators.
• Due to limited space, participation is by invitation only.

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.