University of Cambridge > > Algebra and Representation Theory Seminar > Boundary algebras arising from uniform Postnikov diagams on surfaces

Boundary algebras arising from uniform Postnikov diagams on surfaces

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  • UserColin Krawchuk
  • ClockWednesday 01 December 2021, 16:30-17:30
  • HouseMR12.

If you have a question about this talk, please contact Stacey Law.

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.

This talk is part of the Algebra and Representation Theory Seminar series.

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