Speaker: Maitreyee Kulkarni, Louisiana State University

Title: Categorification of cluster structure on partial flag varieties

Date: 10/25/2016

Time: 1:00 PM - 1:50 PM

Place: C304 Wells Hall

Let G be a Lie group of type ADE and P be a parabolic subgroup. It is known that there exists a cluster structure on the coordinate ring of the partial flag variety G/P (see the work of Geiss, Leclerc, and Schroer). Since then there has been a great deal of activity towards categorifying these cluster algebras. Jensen, King, and Su gave a direct categorification of the cluster structure on the homogeneous coordinate ring for Grassmannians (that is, when G is of type A and P is a maximal parabolic subgroup). In this setting, Baur, King, and Marsh gave an interpretation of this categorification in terms of dimer models. In this talk, I will give an analog of dimer models for groups in other types by introducing a technique called “constructing sheets over Dynkin diagrams”, which can (conjecturally) be used to generalize the result of Baur, King, and Marsh.