Geometric Methods and Langlands Functoriality in Positive Characteristic (1549)
Dates: 11-15 January 2016 at CIRM (Marseille Luminy, France)
The aim of this workshop is to bring together people working on Geometric methods and on Langlands functoriality in positive characteristic with people more used to representation theoretic and automorphic methods.
For example, not many people master yet the theory of Shtukas, especially the one which allowed Vincent Lafforgue recently to prove the global Langlands correspondence in positive characteristic "from automorphic to Galois". The hope is that it could be fruitful to bring these methods together with the themes of the chaire Jean Morlet.
So, one of the main aims of this workshop is to review the recent progress on the Global Langlands program for arbitrary reductive groups in positive characteristic by Vincent Lafforgue which appears in his papers:
(1) V. Lafforgue: Introduction aux chtoucas pour les groupes réductifs et à la paramétrisation de Langlands globale; http://arxiv.org/pdf/1404.3998v2
(2) V. Lafforgue: Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale; http://arxiv.org/abs/1209.5352
Vincent Lafforgue will be a scientific committee member for the workshop and one of the speakers. Other speakers will include Simon Riche and Sergey Lysenko.
We intend the workshop to be open for discussions and spontaneous additional talks, as the aim of the workshop is to understand different topics which come together in this work of Vincent Lafforgue. There is also scope for further work!
(1) Introduction to automorphic forms and the global Langlands program for function fields; similarities and differences with number fields .
(2) Geometric Satake equivalence.
(3) Theory of Shtukas.
(4) Proof of Vincent Lafforgue's theorem.
(5) Relationship with the Geometric Langlands program.