Orbit growth rate in Higher rank Teichmüller spaces

For some non-compact semisimple Lie groups G there are connected 
components of the character variety Hom(\pi_1(S),G)/G that only consist 
of conjugacy classes of injective homomorphisms with discrete image, the 
higher rank Teichmüller spaces. After introducing and motivating the 
study of HRTS, I will discuss joint work with Sambarino and Wienhard in 
which we study how the orbit growth rate of the associated actions on 
the Riemannian symmetric space G/K varies on the different HRTS.