L'étude des sous-groupes discrets des groupes de Lie semi-simples est un domaine qui a une longue histoire et qui est en même temps un sujet de recherche très actif. Elle est au cœur de plusieurs domaines, allant de la géométrie différentielle à la théorie des nombres et, depuis la percée de Margulis dans les années 70, elle est intimement liée aux systèmes dynamiques.

Alors que les développements ultérieurs prennent en compte les phénomènes de rigidité, notre programme se concentrera sur les aspects géométriques des groupes discrets flexibles.

This term focuses on rigidity of group actions with some focus on issues that arise out of Zimmer's groundbreaking work in the 1980's. Areas of interest range from local and global rigidity of group actions to special rigidity phenomena in small dimensions to symmetry groups of geometric structures to measure rigidity results for quite general group actions with hyperbolicity. This broad area has seen a very large number of dramatic breakthroughs in recent years.

The theoretical study of quantum many-body systems is a challenging task due to the amazing complexity induced by the huge number of degrees of freedom of these systems. Equilibrium properties of such systems have been deeply studied in the last decades. In particular, at one-dimension, it is possible for some systems to have access to exact solutions, for instance, within Bethe Ansatz methods. Where exact solutions are not accessible, it is possible to use field theoretical approaches or numerical techniques.