Cluster algebras were introduced by Fomin and Zelevinsky in 2000. Since then, cluster algebras have been discovered in many contexts throughout mathematics. In this talk, we will focus on a subclass "locally acyclic cluster algebras" introduced by Muller. A "locally acyclic cluster algebra" is a cluster algebra which admits a finite cover by acyclic cluster algebras. Many nice properties of acyclic cluster algebras (such as finite generation, equaling their upper cluster algebra, smoothness) extend to locally acyclic cluster algebras. This subclass is pretty large in the sense that it includes the Grassmannian (more generally, all positroid varieties).
Speaker(s): Zenan Fu (University of Michigan)