Pastures, polynomials, and matroids

Matthew Baker
Georgia Institute of Technology
Thursday, February 4, 2021 - 3:30pm to 4:30pm
via Zoom ID 91514486597 (contact faculty for pw)

A pasture is, roughly speaking, a field in which addition is allowed to be both multivalued and partially undefined. I will describe a theorem about univariate polynomials over pastures which simultaneously generalizes Descartes' Rule of Signs and the theory of Newton Polygons. I will also describe a novel approach to the theory of matroid representations which revolves around a universal pasture, called the "foundation", which one can attach to any matroid. This is joint work with Oliver Lorscheid.