In this paper, we describe a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well-studied case of dimer models on a disc. We prove that all Berenstein ...

We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky's cluster algebras and their (additive) categorification via triangulated categories. Journal Information Annals ...

Coxeter theory investigates groups generated by reflections and the geometric structures arising from their actions, such as root systems and Dynkin diagrams. This body of work underpins vast areas of ...