# Session on the Serre conjecture

Date: January 15 - February 14, 2013

Organizers: Luis V. Dieulefait and Jean-Pierre Wintenberger

The aim of the session "Serre's conjecture" was to report on recent works linked to that conjecture, in particular about Galois representations and automorphic representations.

During the weeks which started on January 14 and January 21, Henri Carayol lectured on his work on the algebraic properties of Griffiths-Schmid varieties. The Griffiths-Schmid varieties are analytic varieties classifying Hodge structures. Studying their algebraic properties might be a step towards constructing Galois representations associated to automorphic representations appearing in the cohomology of these varieties.

Our second theme related to the recent work of Michael Harris, Kai-Wen Lan, Richard Taylor and Jack Thorne, who had constructed Galois representations associated to not necessarily self-dual automorphic representations. The proof heavily relies on p-adic properties of automorphic representations.

Michael Harris lectured on January 24, 25 and at the Hausdorff Colloquium on January 23. Kai-Wen Lan lectured during the week January 28 - February 1. Günter Harder lectured on Eisenstein cohomology during the weeks January 21 - 25 and January 28 - February 1.

During the weeks January 21 - 25 and January 28 - February 1, Luis Dieulefait reported on his work, in which, making use of a strategy similar to the one used in the proof of Serre's conjecture, some particular cases of non solvable base change are proved. Jean-Pierre Wintenberger delivered an introductory lecture week January 14 - 18.

See Trimester Seminar for details on the talks.

During the week February 4 - 8, we holded a research conference.