Department of Mathematics

Seminar in Cluster algebras

  •  Maitreyee Kulkarni, Louisiana State University
  •  Categorification of cluster structure on partial flag varieties
  •  10/25/2016
  •  1:00 PM - 1:50 PM
  •  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.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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