Volume of maximal representations into SO(2,3)

Maximal representations from the fundamental group of a surface group into a hermitian Lie group G form connected components of the character variety generalising the Teichmüller space. When G=SO(2,3), those representations act cocompactly on some convex in the pseudo-hyperbolic space (a pseudo-riemannian analogue of the hyperbolic space), and one can define a volume functional on the space of maximal representations. In this talk I will explain a surprising result concerning the boundedness of this volume functional.