Convex projective manifolds are a generalization of hyperbolic manifolds. Koszul
showed that the set of holonomies of convex projective structures on a compact
manifold is open in the representation variety. We will describe an extension of this
result to convex projective manifolds whose ends are generalized cusps, due to
CooperLongTillmann. Generalized cusps are certain ends of convex projective
manifolds. They may contain both hyperbolic and parabolic elements. We will describe
their classification (due to BallasCooperLeitner), and explain how generalized cusps
turn out to be deformations of cusps of hyperbolic manifolds. We will also explore
the moduli space of generalized cusps, it is a semialgebraic set of dimension n^2n,
contractible, and may be studied using several different invariants. For the case of
three manifolds, the moduli space is homeomorphic to R^2 times a cone on a solid
torus.
