Locally free Caldero-Chapoton functions

Locally free Caldero-Chapoton functions are introduced by Geiss-Leclerc-Schröer for locally free representations of certain quivers with relations associated to skew-symmetrizable matrices. They show that for Dynkin types these functions give formulas for cluster variables, generalizing Caldero-Chapoton’s formula in simply laced cases. We extend this formula to rank 2 cluster algebras and those associated to unpunctured marked bordered surfaces with orbifold points. Part of this talk is based on joint work with Daniel Labardini-Fragoso.