Families of identities on hyperbolic surfaces

Hugo Parlier (Luxembourg)

There are a number of so-called "identities" which are equations which relate the lengths of geodesics on a hyperbolic surface to some geometric quantity. Earlier versions of these are due to Basmajian and McShane, the latter of which was generalized by Mirzakhani and used in a spectacular fashion. This talk will be about a new family of identities which generalize Basmajian's identity, and interpolate in some sense between the identities of Basmajian and McShane. This is joint work with Ara Basmajian and Ser Peow Tan.