Andrea Pasquali, Triangulations on orbifold surfaces and skew group algebras.

Abstract:

Cluster algebras arising from surface triangulations are by now a classical and rich theory. It makes sense to study how far this theory can be extended to surfaces with some singularities, for instance orbifold points. In a recent paper, Amiot and Plamondon opened the way by convincingly interpreting the "punctures" of classical cluster algebras from surfaces as "orbifold points of order 2". The connection between the corresponding Jacobian algebras is then given by a skew group algebra construction. Motivated by this, I will speak about skew group algebras of Jacobian algebras in general, explaining what is known and what is difficult. This will hopefully shed some light on the broader problem of constructing algebras from triangulations of orbifold surfaces.