# Algebraic Geometry Group

### Members

Head : Julien Sebag.

Professor Emeritus : Pierre Berthelot, Laurent Moret-Bailly.

Professors : Christophe Mourougane, Matthieu Romagny, Julien Sebag.

Associate professors : Michele Bolognesi, David Bourqui, Lionel Fourquaux, Yongquan Hu, Florian Ivorra, Bernard Le Stum.

CNRS research associates (chargÃ©s de recherches) : Xavier Caruso, FranÃ§ois Charles, Jean-Yves Ã?tesse, Michel Gros.

PhD students : Julien Dhondt, Kodjo Egadédé Kpognon, Jérémy Le Borgne, Cécile Le Rudulier, Charles Savel, Tristan Vaccon.

### General presentation

The research topics of the group cover the following themes:

- 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 rÃ´le; - 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:
*Ã©tale cohomology*,(crystalline and rigid), extension of the theory of modules over rings of differential operators (*p*-adic cohomologies*D-modules*) outside characteristic zero; - development of arithmetic structures related to
;*p*-adic Hodge theory *motivic cohomology*,*mixed motives*and*motivic integration*.

### Activities

The group organizes a weekly seminar on various topics going from algebraic geometry and topology to number theory (organizer: Yongquan Hu) which takes place on Thursdays, from 10:30 to 11:30.

The Geometry Seminar is run jointly by the three IRMAR geometry groups (organizer: Michele Bolognesi).

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

### Conferences organized by members of the team

Upcoming events :

### Networks

Some members of the group are part of the GDR 3064 GÃ©omÃ©trie algÃ©brique complexe.

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

- Positive (Positivity in algebraic, arithmetic and analytic geometry) ;
- Aspects algÃ©brique et analytique de la gÃ©omÃ©trie complexe en dimension supÃ©rieure
- Applications de la gÃ©omÃ©trie de Berkovich.
- Calculs effectifs en thÃ©orie de Hodge p-adique (CETHop)
- Points entiers et points rationnels.