Appears in collection : Structures on Surfaces / Structures sur des surfaces

Fock and Goncharov give parameterisations of two different types of moduli spaces of properly convex real projective structures. I'll discuss a number of observations made about these parameterisations, the geometric structures that are parameterised by them, their relationship with representations into SL(3,R), canonical cell decompositions, and compactifications. This includes joint work with Alex Casella, Robert Haraway, Robert Löwe and Dominic Tate.