VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk
Simonetta Abenda (Università di Bologna)
Wednesday 24th November, 2021 13:30-14:30 Zoom seminar hosted by ICMS
Maximal minors of Kasteleyn sign matrices on planar bipartite graphs in the disk count dimer configurations with prescribed boundary conditions, and the weighted version of such matrices provides a natural parametrization of the totally non--negative part of real Grassmannians. In this talk I will explain the relation between this variant of Kasteleyn theorem and the spectral problem for the family of real regular KP multi-soliton solutions: indeed the KP wave function solves Kasteleyn system of relations at the nodes of the spectral curve if the dual graph of the latter represents the soliton data. The talk is based on the results of a project in collaboration with P.G. Grinevich (Steklov Institute, Moscow).
For more information, and how to access the seminar through Zoom, see the webpage of the events here.