Seminar

I will begin with `cluster localizations', localizations of cluster algebras which are still cluster algebras. Geometrically, a cluster localization of A is dual to an open subscheme of Spec(A) with a cluster structure. Many properties of a cluster algebra can be studied locally with respect to these open patches. This local approach is very effective for `locally acyclic cluster algebras'. In this talk, I will define this class, review some of their important properties, give several examples, and present an algorithm for demonstrating that a given cluster algebra is locally acyclic.