Summer School on Serre's Modularity Conjecture

_{Luminy, July 9-20, 2007}

This summer school is addressed to confirmed researchers as well as to younger colleagues with a good background in arithmetic geometry. Its principal objective is to present a proof of Serre's conjecture on the modularity of irreducible odd representations of the absolute Galois group G_Q of the field of rational numbers on two-dimensional vector spaces over finite fields.


We plan to offer a course on the recent proof of the conjecture due to Khare and Wintenberger. We are also planning courses on the following subjects, which are essential ingredients in the proof:

• Base change for GL(2),
• Galois representations associated to  classical and  Hilbert modular forms,
• Equivalence between the weak form and the strong form of Serre's conjecture,
• Lifting and modular lifting theorems,
• p-adic Hodge theory, 
• Potential modularity theorems,
• Compatible families of l-adic representations.

If time permits, there will be additional lectures, possible on the modularity of two-dimensional irreducible geometric l-adic representations of G_Q. The subject is in a state of flux and a more detailed program will be provided at a later date.

List of participants

Organization's committee

• Pierre COLMEZ (Ecole Polytechnique, Palaiseau, France),
• David ELLWOOD (Clay Mathematics Institute, U.S.A),
• Jean-Marc FONTAINE (Université de Paris XI, Orsay, France),
• Michael HARRIS (Université de Paris VII, France),
• Mark KISIN (University of Chicago, U.S.A.),
• Richard TAYLOR (Harvard University, U.S.A.).

Programme

Practical informations :

The school will be held at Centre International de Rencontres Mathématiques. Participants will have the use of resources at CIRM, such that the library and the computing facilities. will be housed at the CIRM and the other half in some recently renovated rooms at a student dormitory close to the CIRM. All meals will be served at CIRM. The first meal served at CIRM shall be the dinner of Sunday July 8 (buffet froid) and the last one the dinner of Friday July 20. There will be no lunch and no dinner on Saturday 14 and no lunch on Sunday 15 (it should be possible to get a lunch box for Saturday's lunch. During the week-end, reasonably priced meals are available on Luminy's campus).

Rates:

• single room at the CIRM: 38,11 € per night,
• double room at the CIRM: 30,11 € per night, per person,
• single room ("studette") in the student dormitory: about 16 € per night (student rate), about 26€ per night (regular rate) [exact rates will be very close to this estimate but will be known only very shortly before the summer school).
• breakfast: 4 €
• other meal: 13,25 &euro.

We hope not to require a registration fee. We expect founding notably from the CIRM (via the CNRS, the SMF and some local institutions), from the ANR and from the Clay Mathematical Institute. We hope to be able to cover the living expenses of a substantial number of participants, but all of those who have the possibility to find their own founding are highly encouraged to do so. We expect most of the participants to cover their own travel expenses, but those who may have serious difficulties should let us know. In a limited number of cases, we should be able to cover, at least partly, some travel expenses. This summer school is an official activity of the Research Training Network "Arithmetic Algebraic Geometry" of the European Community. The members of this network are requested to ask their node coordinator to take care of their living and travel expenses.

You may download the poster of the Summer School .

Registration is now closed.

Sponsors :

Agence Nationale de la Recherche

Centre National de la Recherche Scientifique

Clay Mathematics Institute

Réseau européen "Arithmetic Algebraic Geometry"

Institut Universitaire de France

Fondation Hugot du Collège de France

Université de Paris XI

Ecole Polytechnique - Palaiseau

Japan Society for the Promotion of Science

C.I.R.M