# Summer School on the Arithmetic of the Langlands Program

**Dates:** May 08 - 12, 2023

Venue: Lipschitz-Saal (Endenicher Allee 60, Bonn)

Organizers: Frank Calegari (Chicago), Ana Caraiani (London), Laurent Fargues (Jussieu), Peter Scholze (Bonn)

The school is co-financed by the Gottfried Wilhelm Leibniz Prize of Peter Scholze, awarded by the German Research Foundation (DFG).

**Description: **This school provides an introduction to some of the main topics of the trimester program. It is mainly directed at PhD students and junior researchers.

Automorphy Lifting: Patrick Allen (Montreal), James Newton (Oxford)

Categorical Local Langlands: Toby Gee (London), Xinwen Zhu (Stanford)

p-adic Automorphic Forms: George Boxer (London), Lue Pan (Princeton), Vincent Pilloni (Paris)

p-adic Geometry: Judith Ludwig (Heidelberg), Arthur-Cesar le Bras (Paris)

Shtukas: Eva Viehmann (Münster), Cong Xue (Paris)

Click here for the schedule.

Click here for the abstract

The application deadline has expired and the platform has been closed.

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.

# Video Recordings

# Monday, May 8

Judith Ludwig - p-adic Geometry, 1: Adic and perfectoid spaces

Xinwen Zhu - Categorical local Langlands, 1

Cong Xue - Shtukas, 1

Patrick Allen - Automorphy Lifting, 1

# Tuesday, May 9

George Boxer - p-adic Automorphic Forms, 1

Cong Xue - Shtukas, 2

Judith Ludwig - p-adic Geometry, 2: Topologies, diamonds and the Fargues-Fontaine curve

Toby Gee - Categorical local Langlands, 2

Arthur-César le Bras - p-adic Geometry, 3: Vector bundles on the FarguesFontaine curve

# Wednesday, May 10

Eva Viehmann - Shtukas,3

James Newton - Automorphy Lifting, 2

# Thursday, May 11

Vincent Pilloni - p-adic Automorphic Forms, 2

Toby Gee - Categorical local Langlands, 3

Patrick Allen - Automorphy Lifting, 3

Arthur-César le Bras - p-adic Geometry, 4: BanachColmez spaces

Eva Viehmann - Shtukas, 4

# Friday, May 12

James Newton - Automorphy Lifting, 4

Lue Pan - p-adic Automorphic Forms, 3

Xinwen Zhu - Categorical local Langlands, 4