Expansion formulae for quasi-cluster algebras

Introduced by Dupont and Palesi, quasi-cluster algebras are cluster structures arsing from ‘triangulated’ non-orientable surfaces. Specifically, each cluster variable corresponds to the (laminated) lambda length of an arc on the surface. Fixing an initial triangulation, and therefore an initial set of cluster variables, one can express any subsequent cluster variable in terms of the initial ones. In this talk we will investigate the behaviour of these expressions. In particular, following the work of Musiker, Schiffler and Williams we will assign certain graphs to arcs on the surface. In doing so, we find expansion formulae of the cluster variables in terms of perfect matchings of these graphs. The talk is for a general audience -- no prior knowledge of cluster theory will be assumed.