Abstract:The deformation space of representations of the fundamental group of a surface in a Lie group enjoys rich geometric, algebraic and topological structure, some of which is invariant under the mapping class group of the surface. I will survey how the symplectic geometry of these moduli spaces relates invariant theory of the Lie group with the topology of curves on the surface, leading to a new proof of ergodicity of the mapping class group on SU(2)-representations.