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
of the field of rational numbers on two-dimensional vector spaces over
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),
representations associated to classical and Hilbert
- Equivalence between the weak form and the strong form of
- 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
. The subject is in a state of flux and a
more detailed program
will be provided at a later date.
- Pierre COLMEZ (Ecole Polytechnique, Palaiseau, France),
- David ELLWOOD (Clay Mathematics Institute, U.S.A),
- Jean-Marc FONTAINE (Université de Paris XI,
- Michael HARRIS (Université de Paris VII, France),
- Mark KISIN (University of Chicago, U.S.A.),
- Richard TAYLOR (Harvard University, U.S.A.).
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
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
- single room at the CIRM: 38,11 € per night,
- double room at the CIRM: 30,11 € per night, per
- 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
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.
Nationale de la Recherche
Centre National de
la Recherche Scientifique
européen "Arithmetic Algebraic Geometry"
Universitaire de France
Fondation Hugot du Collège
de Paris XI
Polytechnique - Palaiseau
for the Promotion of Science