"Representations of Surface Groups and higher Teichmueller spaces"

Abstract: I will introduce maximal representations, which are special
homomorphisms of the fundamental group of a surface into simple Lie
groups of Hermitian type. Maximal representations into SL(2,R) are
precisely the holonomy representations of complete hyperbolic
structures on the surface.  In general maximal representations have
many nice geometric properties, e.g.  they are always faithful with
discrete image, which suggests that their moduli space give some
higher analogue of Teichmueller space. If time permits I will also
discuss the relations to other higher Teichmueller spaces studied by
Hitchin, Labourie, Fock and Goncharov. This is joint work with
M. Burger and A. Iozzi.