Presentation.

This project ANR-11-BS01-013: DiscGroup, Facettes des groupes discrets.
Geometric group theory emerged as a feld after work by M. Gromov, G. Mostow, G. Margulis, W. Thurston and others, where one deduces algebraic properties of groups from geometric and dynamical properties of actions of these groups. An exemplary result of this kind is Gromov's polynomial growth theorem saying that a group whose balls in its Cayley graph grow polynomially is virtually nilpotent. This theory involves many viewpoints, including geometric, dynamical, probabilistic, analytic ones. Presently, great progress is being made in this area with, for instance, the solution of Tarski's problem about the 1st order theory of free groups, or of the ending lamination conjecture for ends of hyperbolic 3-manifolds, or on the theory of approximate groups and its relation to expansion properties of fnite groups.
The goal of this project is to gather and federate a group of researchers working on discrete groups from geometric, analytic, dynamical, and logical perspectives. These points of view are very much complementary to each other, and one of the objectives of this project is to share ideas among this group of people.

Members of the project