Degeneration of convex projective structures on surfaces.

The Thurston construction for the compactification of Teichmuller spaces is only a particular case of a more general construction that can be used to construct compactifications of the variety of characters of representations of a finitely generated group in SL_n(R). Both the construction of the boundary and the interpretation of boundary points can be made using the so-called Tropical Geometry. In the particular case of SL_3(R) we get a compactification of the space of convex projective surfaces.