Algebraic Geometry Seminar

Friday, September 20, 2019, 3:15pm, 119 Physics
Matt Baker (Georgia Tech, Mathematics)
The Moduli Space of Matroids

Abstract:

I will begin with an introduction to hyperfields (originally introduced by Krasner for number-theoretic reasons), and then discuss a far-reaching generalization, Oliver Lorscheid’s theory of ordered blueprints. Two key examples are the sign hyperfield S and the tropical hyperfield T. I will discuss a common generalization, in this language, of Descartes' Rule of Signs (which involves polynomials over S) and the theory of Newton Polygons (which involves polynomials over T). I will then give a quick introduction to matroids and explain how the theory of ordered blueprints and ordered blue schemes allow us to construct a "moduli space of matroids", which can be viewed as an enhancement of the usual Grassmannian variety in algebraic geometry. This is joint work with Oliver Lorscheid.

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