It is a classical result that a discrete faithful representation of a surface group into PSL(2,R) is determined by the lengths of the images of finitely many simple curves on the surface. More generally, Dal'bo and Kim showed that a Zariski dense representation of a group into a simple Lie group G is determined, up to automorphisms of G, by the lengths of the images of all its elements. We will discuss this result and a recent result of Bridgeman, Canary, and Labourie that a representation of a surface group into PSL(3,R) in the Hitchin component of holonomies of convex projective surfaces is determined up to conjugacy by the length of images of simple closed curves. Speaker(s): Richard Canary (University of Michigan)