Pastures, Polynomials, and Matroids

Matt Baker (Georgia Tech)

02-Apr-2021, 19:00-20:00 (22 months ago)

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 $\mathbf{F}_1$ 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 Newton polygons. 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.

algebraic geometry

Audience: researchers in the topic

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Stanford algebraic geometry seminar

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