Cambrian combinatorics and cluster combinatorics

David Speyer

I will explain a project, begun by Nathan Reading and continued by Reading and myself, to describe the combinatorics of cluster algebras by describing certain "Cambrian" congruence relations on Coxeter groups. I will explain what Cambrian congruences are and how we can use them to read off cluster data such as B-matrics, g-vectors and quasi-Cartan companions.