Pastures, Polynomials, and Matroids

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

( video )

Comments: The discussion for Matt Baker’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-04-02-mb (and will be deleted after ~3-7 days).

---

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

---