On the parameter spaces of projective structures on surfaces and their compactification

I will introduce projective structures on surfaces and their
Teichmuller-like parameter spaces. I will present a construction of
compactification for these parameter spaces that is similar to the
Thurston compactification of Teichmuller spaces, constructed using
tropical geometry. Then I will discuss some results about this
compactification that are part of a work in progress, joint with S.  Choi
and C. Manon.