A thematic trimester in arithmetic will take place in ENS de Lyon and Université Lyon 1 from April 23, 2018 to June 29, 2018. This trimester is divided in two parts with different focus, with a conference taking place from May 22 to May 25.

The first part of the trimester focuses on the theory of algebraic groups, and particularly the Grothendieck-Serre conjecture on locally trivial homogeneous principal spaces. The conjecture was proved by Fedorov and Panin, following work of Colliot-Thélène, Nisnevich, Ojanguren, Ragunathan, Stavrowa, Vavilov...In the arithmetic case, Fedorov proved recently a significant special case of the conjecture. The study of this problem uses, among others, approximation techniques in algebraic groups, patching techniques, and affine grassmanians.

The second part of trimester focuses mainly on the question of the geometrization of the local Langlands correspondence. This problem was born from three major advances in arithmetic geometry: the introduction of the theory of perfectoid spaces by Scholze, the work of V. Lafforgue on the Langlands correspondence for function fields, and the introduction by Fargues and Fontaine of the fundamental curve of p-adic Hodge theory. We will take stock of the latest advances.

The first half of the semester (from April 23 to May 20) will take place in Institut Camille Jordan, Université Lyon 1, in the Braconnier building on the La Doua campus in Villeurbanne. See here for access information. The closest tramway station is the "Université Lyon 1" stop on line T1.

The conference and the second half of the semester (from May 21 to June 30) will take place in UMPA, the mathematics department of ENS de Lyon, in the Gerland neighborhood of Lyon. See here for access information. The closest subway station is the "Debourg" stop on line B, and the closest tramway station is the "ENS Lyon" stop on line T1.

Here is the website of the public transportation in Lyon, with maps.

From May 22 to May 25:

Midpoint conference in ENS de Lyon. Invited speakers :

Joseph Ayoub,  Kestutis Cesnavicius, Vladimir Chernousov, Najmuddin Fakhruddin, Roman Fedorov, Javier Fresan, Michael Harris, Tasho Kaeltha, Arthur-Cesar Le Bras, George McNinch, Sophie Morel, Igor Rapinschuk, Alexander Smith, Nicolas Templier, Jared Weinstein, Fei Xu

From May 28 to June 29:

Mini-courses on the geometrization of the Langlands correspondence: introductive courses (local Langlands program, Rapoport-Zink spaces, Shimura varieties, perfectoids and diamonds), courses on the conjecture (works of Fargues, Scholze, Caraiani-Scholze), perspectives (p-adique Langlands correspondence and cohomology of Rapoport-Zink spaces, Emerton-Gee stack).

• Ana Caraiani
• Gabriel Dospinescu
• Laurent Fargues
• Philippe Gille
• Roman Fedorov
• Toby Gee
• Diego Izquierdo
• Tasho Kaletha
• Arthur-César Le Bras
• Sophie Morel
• Andrei Rapinchuk
• Michael Rapoport
• Benoît Stroh
• Olivier Taibi
• Jared Weinstein

Pierre Colmez, Laurent Fargues, Toby Gee, Michael Harris, Sophie Morel, Michael Rapoport

Laurent Berger, Gabriel Dospinescu, Philippe Gille, Wieslawa Niziol, Vincent Pilloni, Sandra Rozensztajn, Amaury Thuillier