Talk page
Title:
Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk
Speaker:
Abstract:
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 show that this variant of Kasteleyn theorem is equivalent to the geometric construction in Abenda-Grinevich (arXiv:1908.07437). I will then use Kasteleyn system of relations to solve the spectral problem for the family of KP multi-soliton solutions. Indeed the KP wave function solves such system at the nodes of the spectral curve if the dual graph of the latter represents the soliton data. The talk is mainly based on the results in arXiv:2012.13797 and this research is part of a project in collaboration with P.G. Grinevich (Steklov Institute, Moscow).
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