Kayla Wright
(University of Minnesota)

Mathematics Seminar

In this talk, we will discuss joint work with Moriah Elkin and Gregg Musiker about a combinatorial model for certain Grassmannian cluster algebras. The Grassmannian Gr(k,n) of k-planes in **C**^n, , has a cluster structure that is not well-understood for k>2. In these algebras, Plücker coordinates ∆*I give us a subset of the cluster variables and have lovely combinatorial descriptions. However, most cluster variables are more complicated expressions in Plücker coordinates and lack such a combinatorial description. In our work, we give a graph theoretic interpretation for the Laurent expansion of cluster variables of low degree in terms of higher dimer models. This work employs SL*k web combinatorics and we conjecture these webs are the key ingredient to understanding Grassmannian cluster algebras. If time permits, I would like to also pose an open problem I hope to work on (possibly with the algebraic power of Aarhus postdocs) relating our dimer combinatorics to the categorification of Grassmannian cluster algebras.

Organised by: AarHomAlg