Programm des Emmy-Noether-Seminars

Fri, 03.02.2017, 14:30

End:
Fri, 03.02.2017, 15:30
Dimer models and Grassmannian categories
Emmy-Noether-Seminar

Speaker: Prof. Dr. Karin Baur (Graz)
Host: Knop
Room: 04.363

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.

This is joint work with A. King and R. Marsh.