researchseminars.org

Matt Baker (Georgia Institute of Technology)
2021-01-22 14:15 - 15:30 UTC | https://researchseminars.org/talk/TGiZ/14/
Title: Pastures, Polynomials, and Matroids (https://researchseminars.org/talk/TGiZ/14/)
by Matt Baker (Georgia Institute of Technology) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z

Abstract
A pasture is, roughly speaking, a field in which addition is allowed to be both multivalued and partially undefined. Pastures are natural objects from the point of view of F_1 geometry and Lorscheid’s theory of ordered blueprints. I will describe a theorem about univariate polynomials over pastures which simultaneously generalizes Descartes’ Rule of Signs and the theory of NewtonPolygons. Conjecturally, there should be a similar picture for several polynomials in several variables generalizing tropical intersection theory. I will also describe a novel approach to the theory of matroid representations which revolves around a canonical universal pasture called the “foundation” that one can attach to any matroid. This is joint work with Oliver Lorscheid.
