Algebraic Combinatorics Seminar - Nick Early

Title: From weakly separated collections to matroid subdivisions

Abstract:

We study arrangements of slightly skewed tropical hyperplanes, called blades, on the vertices of a hypersimplex $\Delta_{k,n}$. We reformulate the condition under which such an arrangement induces a matroid (in fact a positroid) subdivision as the requirement that the collection of vertices defines a weakly separated collection of k-element subsets, in the sense of the work of Leclerc and Zelevinsky on quasicommuting families of quantum minor.

This talk is based on 1910.11522 and 1810.0324.