Algebraic Geometry Group

Members (2009-2010)

Professors : Antoine Chambert-Loir (IUF member; for 2009-2010, see his web page at the IAS in Princeton), Laurent Moret-Bailly, Christophe Mourougane, Julien Sebag.

Associate professors : David Bourqui, Gweltaz Chatel (INSA), Lionel Fourquaux, Florian Ivorra, Bernard Le Stum, Anne Virrion.

CNRS research professor (directeur de recherches) : Ahmed Abbes.

CNRS research associates (chargés de recherches) : Xavier Caruso, Jean-Yves Étesse, Michel Gros.

PhD students : Davide Alessio, Damian Brotbek, Viviana Delanoy, Mathilde Herblot, Jérémy Le Borgne, Noël Le Du, Rodolphe Richard.

Recent members;: Pascal Autissier (professor at Bordeaux I since September 2009), Daniel Conduché (retired).

Positions

Two positions of Maîtres de conférences (associate professors) will be open for September 2010. Any mathematician interested in applying is invited to contact members of the Algebraic geometry team, or the other two teams of Irmar devoted to geometry.

General presentation

Most of the research of the group lies within arithmetical algebraic geometry: study of algebraic varieties over number fields, or their rings of integers, over local fields, over fields of positive characteristic, and their applications in number theory. It is possible to split them in a few groups:

study of algebraic, rational or integral points of some algebraic varieties, in particular their height and their distribution; applications to “arithmetical dynamical systems”. The ideas and the techniques of Arakelov geometry play an important rôle;
more geometric questions, related to moduli problems (foundation of the theory of algebraic stacks, covers of curves, torsors) and their arithmetical applications;
development of cohomological methods used in arithmetic geometry: étale cohomology, p-adic cohomologies (crystalline and rigid), extension of the theory of modules over rings of differential operators (D-modules) outside characteristic zero, and also motivic cohomology.

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Activities

The group organizes a weekly seminar on various topics going from algebraic geometry and topology to number theory (organizer: Florian Ivorra) which takes place on Thursdays, from 10:30 to 11:30. Ask for the program !

The geometry seminar is run jointly by the three IRMAR geometry groups (organizer: Goulwen Fichou).

The group also takes part in the organization of the weekly cryptography seminar.

Networks

Some members of the group are part of the GDR 3064 Géométrie algébrique complexe.

Some members of the group take part in various projets of the Agence nationale de la recherche :

Diophante ;
Aspects algébrique et analytique de la géométrie complexe en dimension supérieure
Applications de la géométrie de Berkovich.
Points entiers et points rationnels.

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