Divisible convex sets with properly embedded cones

An open subset of real projective space is said to be properly convex if it is contained in an affine chart where it is convex and bounded. Together with their natural Hilbert metric and group of projective symmetries, properly convex sets are a rich source of geometry, dynamics, and group theory. Of particular interest are those that are divisible, that is, they admit a compact quotient by a discrete group of symmetries. In general, it is a challenging problem to construct such examples. After reviewing the global classification scheme, I will describe a new class of examples of divisible convex sets with special geometric properties (non-symmetric and non-strictly convex) that completes a missing part of the picture. This is joint work with Pierre-Louis Blayac.