Higher rank counting problems

Let \Gamma be a discrete group of isometries of a symmetric space X. The orbital counting problem consists on finding an asymptotic for #{g in \Gamma: d_X(o,g o)\leq T} as T goes to infinity, where o is a given point on X. The purpose of the lecture is to discuss this problem for a class of subgroups that contains Hitchin representations of surface groups. The novelty of this situation is that even when one restricts the problem to the ‘convex core,’ the group still has infinite co-volume.