This talk will be about the theory of compactification of the character variety.
Methods coming from algebraic geometry and tropical geometry can be
used to construct and to study some of these compactifications. With
these methods it is often possible to get some results by direct
computations. We will mostly discuss the special case of deformation
spaces of convex real projective structures on open surfaces, a subset
of the character variety of the free group in SL(3,R).
This is joint work with S. Choi.
 

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