Programm des Emmy-Noether-Seminars
Fri, 03.02.2017, 14:30
Fri, 03.02.2017, 15:30
Dimer models and Grassmannian categories
Speaker: Prof. Dr. Karin Baur (Graz)
In this talk, I will illustrate the cluster structure on a coordinate ring of a Grassmanniann. Then I will explain how to get a categorical version of the cluster structure on the Grassmannian, using dimer models.
A dimer model can be defined as a quiver embedded into a surface in such a way that the complement is a disjoint union of disks with oriented boundaries. Such models can also be considered in the case of a surface with boundary. Postnikov diagrams are used by Scott to describe the
cluster structure of the homogeneous coordinate ring of the
Grassmannian. These diagrams give rise to dimer models on a disk and to a
natural (Jacobian) algebra. We use an idempotent subalgebra to get a categorical version of the cluster structure on the Grassmannian.