Basmajian-type inequalities for maximal representations

Basmajian's celebrated identity gives a way to compute the length of the
boundary of a hyperbolic surface in terms of the lengths of the so-called
orthogeodesics (geodesics orthogonal to the boundary at both endpoints).
This identity can be generalized to the context of maximal representations.
This is a class of representations of the fundamental group of a surface
that can be seen as a generalization of Teichmüller space. I will describe
the classical identity, introduce maximal representations and discuss
Basmajian's identity in this setup. Joint work with Beatrice Pozzetti.