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Algebraic Groups and Geometrization of the Langlands Program
From April 23, 2018 to June 29, 2018
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. Organizing committee
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.
- Laurent Berger (UMPA / ENS de Lyon)
- Gabriel Dospinescu (UMPA / ENS de Lyon)
- Philippe Gille (ICJ / Lyon 1)
- Wieslawa Niziol (UMPA / ENS de Lyon)
- Vincent Pilloni (UMPA / ENS de Lyon)
- Sandra Rozensztajn (UMPA / ENS de Lyon)
- Amaury Thuillier (ICJ / Lyon 1)
Scientific committee
- Pierre Colmez (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6 / France)
- Laurent Fargues (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6 / France)
- Toby Gee (Imperial College London / Royaume-Uni)
- Michael Harris (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6 / France)
- Sophie Morel (Princeton University / USA)
- Michael Rapoport (Université de Bonn / Allemagne)
Guest speakers
- Ana Caraiani (Université de Bonn / Allemagne)
- Pierre Colmez (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6 / France)
- Jean-François Dat (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6 / France)
- Laurent Fargues (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6/ France)
- Roman Fedorov (Université de Pittsburgh / USA)
- Toby Gee (Imperial College London / Royaume-Uni)
- Michael Harris (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6/ France)
- Tasho Kaletha (Université du Michigan / USA)
- Arthur-César Le Bras (ENS Paris / France)
- Sophie Morel (Princeton University / USA)
- Michael Rapoport (Université de Bonn / Allemagne)
- Peter Scholze (Université de Bonn / Allemagne)
- Benoît Stroh (Institut de Mathématiques de Jussieu / Université Pierre et Marie Curie – Paris 6 / France)
- Olivier Taibi (Imperial College London / Royaume-Uni)
- Jared Weinstein (Université de Boston / USA)