Jan Grabowski (Lancaster University) – Categorifying and quantizing cluster ensembles

Cluster ensembles were introduced by Fock and Goncharov to encode seed data for cluster algebras in terms of certain lattices, enabling the definition of cluster varieties by gluing the associated tori. We will explain aspects of two pieces of joint work, with Gratz and Pressland respectively, in which we show that categorifications of cluster algebras yield cluster ensembles, that these categorifications are often quantizable and that there is also a category governing interactions between cluster ensembles. Furthermore, these structures can help us understand mirror symmetry for cluster varieties.