Abstract

A Postnikov diagram is an embedding of oriented curves, called strands, in a disk. These diagrams are known to describe the cluster algebra structure of open positroid varieties, with diagrams of uniform type corresponding to a cluster of minors in the Grassmannian Gr(k,n). Each Postnikov diagram can be associated with a dimer algebra, which is the Jacobian algebra of a quiver with potential. Baur-King-Marsh showed that the opposite of the boundary algebra corresponding to such a dimer algebra is isomorphic to a quotient of the preprojective algebra used by Jensen-King-Su to categorify the cluster structure of Gr(k,n). They also determined the boundary algebra for degree two weak Postnikov diagrams arising from general surfaces. This talk will discuss a combinatorial approach to calculating the boundary algebra associated to a uniform Postnikov diagram, and how this can be translated to Postnikov diagrams on other surfaces.