Felipe Rincón: Tropicalising principal minors of positive definite matrices

Abstract: We study the tropicalisation of the image of the cone of positive definite matrices under the principal minor map. This polyhedral complex is a subset of the set of M-concave functions on the discrete n-dimensional hypercube, and we show that it can be characterised as those functions that lie in the tropical flag variety, or equivalently, in a certain slice of the tropical Grassmannian. This is joint work with Abeer Al Ahmadieh, Cynthia Vinzant, and Josephine Yu.