Combinatorics Seminar- Plabic R-Matrices

Speaker: Sunita Chepuri, University of Minnesota

Title:  Plabic R-Matrices
Abstract:  Postnikov's plabic graphs in a disk are used to parametrize totally nonnegative Grassmannians. One of the key features of this theory is that if a plabic graph is reduced, the face weights can be uniquely recovered from boundary measurements. On surfaces more complicated than a disk this property is lost. In this talk, we investigate a certain semi-local transformation of weights for plabic networks on a cylinder that preserves boundary measurements. We call this a plabic R-matrix. We explore the properties of the plabic R-matrix, including the symmetric group action it induces on plabic networks and its underlying cluster algebra structure.