Triple Dimers and Grassmannian Cluster Algebras
Abstract: In this talk, we will discuss some work in progress with Moriah Elkin and Gregg Musiker about a combinatorial model for Grassmannian cluster algebras in the case of Gr(3,n). In Grassmannian cluster algebras, many cluster variables are quite nice and are given by Plücker coordinates. However, some cluster variables are more mysterious and are given by relatively hard to predict combinations of Plücker coordinates. In our work, we model cluster variables as certain superimpositions of dimer configurations on the associated plabic graph. In particular, in certain Grassmannians, we are able to model these more unwieldy cluster variables using our dimer configurations by using the language of webs.
