Speaker: P. Grinevich (Moscow State University, MIAN)
Date and time: 11.05.2022, 17:00 (GMT +03:00)
Title: Signatures on plabic graphs and completely non-negative Grassmannians II
Abstract: This is a continuation of the talk on 13.04.2022.
As shown by A. Postnikov the cells of completely non-negative Grassmannians can be rationally parametrized by graphs embedded in a disk with positive weights on the edges. In this case the matrix elements representing the Grassmannian points are given as sums along all possible paths from the boundary sources to the boundary sinks. An alternative approach is to define the Grassmannian points by solving a system of linear equations corresponding to the vertices of the graph. In this case positivity is achieved only with the correct choice of signs on the edges called a signature. T. Lam proved the existence of a signature consistent with the property of complete positivity without presenting it explicitly. We give an explicit construction and prove the uniqueness of such a signature up to the action of the natural gauge group.
The report is based on joint work with S. Abenda.
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