This research school consists on an introduction to the geometry of hyperbolic groups and their representations. The global objective is to understand how the intrinsic geometry of the hyperbolic group interacts with the geometry of the target group.
When the hyperbolic group is a surface group, several target groups are subject of major deep results : Teichmüller-Thurston Theory (associated to the groups PSL_2(R) and PSL_2(R) ) and the ‘absence’ of geometric meaning due to Goldman for SU(2), just to name a few. Representations of a general hyperbolic group into a semisimple higher rank Lie group is a current topic of research.
The school consists on 5 mini-courses to be held in english : an introductory course, a course on the large scale geometry of hyperbolic groups, Quasi-Fuchsian representations, representations of surface groups on SU(2) and a course on matrix groups over a p-adic field.