The 1st meeting took place on Monday 13th November 2006 in the Institut Henri Poincaré in Paris. The schedule was

9.30-9.45 | Gathering at the IHP | |

9.45-10.00 | Brief opening remarks | |

10.00-11.00 | Fred Diamond (King's College London)The weight part of Serre's conjecture for Hilbert modular formsAbstract: I will explain the statement of a generalization of Serre's conjecture on modulo p Galois representations to the context of Hilbert
modular forms. The emphasis will be on the recipe (conjectured by
Buzzard, Jarvis and myself) for the set of possible weights, much of
which has now been proved by Gee. I will also discuss some features of
the set of weights in some special cases:1) for representations tamely ramified at primes over p, a phenomenon
which was interpreted conceptually and generalized to GL_{n} by
Herzig ;2) for representations that could be called ”moins ramifiee” at primes over p, a phenomenon which should be related to properties of the
corresponding representations of p-adic groups (via a hypotheticallocal
Langlands modulo p). | |

11.00-12.00 | Informal discussions (and visit to the CNRS for the participants from England) | |

12.00-2.00 | Lunch at École Normale Supérieure | |

2.00-3.00 | Florian Herzig (IHES)A Serre-type conjecture for the weights of tame n-dimensional modulo p Galois
representationsAbstract: I will discuss the weights in a Serre-type conjecture for n-dimensional mod p Galois representations ρ of the absolute Galois
group of Q that are tamely ramified at p. The weight in this context
is an irreducible mod p representation of Γ=GL_{n}(F_{p}).
The conjecture
predicts the weights in which ρ arises in terms of the reduction mod p
of a characteristic 0 representation of Γ associated to ρ restricted to the
inertia subgroup at p. It refines, and is more conceptual than, a previous
conjecture of Ash, Doud, Pollack, and Sinnott. Some theoretical
evidence arising from automorphic representations on GL_{4} is discussed.
| |

3.00-3.30 | Break | |

3.30-4.30 | Toby Gee (Imperial College London)On crystalline representations and the weights in Serre's conjectureAbstract : We discuss the relationship between various generalisations of the weight part of Serre's conjecture, crystalline representations, and modularity lifting theorems. |

The talks took place in the Amphithéâtre Darboux, Institut Henri Poincaré.

The organizers of the meeting were:
Michael Harris (`harris@math.jussieu.fr`),
Guy Henniart (`guy.henniart@math.u-psud.fr`),
Marc Hindry (`hindry@math.jussieu.fr`),
Ariane Mezard (`mezard@math.uvsq.fr`),
Jacques Tilouine (`tilouine@math.univ-paris13.fr`).

Second meeting (London, 02/05/2007)

Main page of the London-Paris Number Theory Seminar

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