Title: Webs, dimers, and total positivity
Speaker: Chris Fraser (IUPUI)
Abstract: I will formulate a higher-rank version of the boundary measurement map for weighted planar bipartite networks in the disk. This map sends a network to a linear combination of SLr tensor invariants known as webs, and is defined using the r-fold dimer model on the network. When r equals 1, our map is Postnikov's boundary measurement used to coordinatize positroid strata. The main result is that the higher rank map factors through Postnikov's map. As a corollary, we deduce a complete set of diagrammatic relations between SLr webs, reproving a result of Cautis-Kamnitzer-Morrison in the classical (q=1) setting. We establish compatibility between our map and restriction to positroid strata. This is joint with Thomas Lam and Ian Le.
Seminar URL: https://people.math.osu.edu/anderson.2804/gcis/