Geometric group theory is a relatively new line of research on its own, inspired by pioneering works of M. Dehn, G.D. Mostow and M. Gromov. It is mainly devoted to the study of countable groups by exploring connections between algebraic properties of such groups and geometric properties of spaces on which these groups act, such as the deck transformation group of a Riemannian manifold. Geometric group theory is a very broad area, and this program aims at introducing young students to different aspects of the theory.
Starting from classical results such at the Mostow rigidity theorem, we intend to build a body of knowledge to the students by introducing them to some basic material concerning hyperbolic geometry, quasi-isometry invariants and amnability, and to several modern aspects of geometric grop theory: word hyperbolic groups, boundary theory, ergodic theory and representations.
Langue officielle de l'école : anglais