I will explain in this talk how to generalise the McShane-Mirzakhani identities in hyperbolic geometry to the more general context of arbitrary cross ratios. Cross ratios appears naturally in the context of Hitchin representations of surface groups to PSL(n,R). Then the identities relate quantities associated to an element of the fundamental group -- representing a simple geodesic -- to quantities associated to rank 2 free groups -- asociated to pair of pants. These last quantities can be computed in Fock-Goncharov coordinates -- a generalisation of Thurston shear coordinates.

This is a joint work with G. McShane.

Lecture #12591

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