The boundary algebra of a dimer model derived from a Postnikov diagram may be used to obtain an additive categorification of the cluster algebra of the associated positroid variety. The boundary algebra has an explicit description in the case of Grassmannians but not for more general positroids. It is known that every Postnikov diagram is move equivalent to one which comes from a Le-diagram and has an isomorphic boundary algebra. We use the perfect matching structure of a dimer model derived from a Le-diagram to provide an algorithm for computing the Gabriel quiver and relations of its boundary algebra.
This video was part of the Maurice Auslander International Conference.
