The moduli space of matroids

Abstract: Matroids are combinatorial gadgets that reflect properties of linear algebra in situations where this latter theory is not available. This analogy prescribes that the moduli space of matroids should be a Grassmannian over a suitable base object, which cannot be a field or a ring; in consequence usual algebraic geometry does not provide a suitable framework. In joint work with Matt Baker, we have used algebraic geometry over the so-called field with one element to construct such moduli spaces. As an application, we streamline various results of matroid theory and find simplified proofs of classical theorems, such as the fact that a matroid is regular if and only if it is binary and orientable.

We will dedicate the first part of this talk to an exposition of matroids. Then we will briefly outline how to construct the moduli space of matroids. In a last part, we will explain with some care why this theory is useful to simplify classical results in matroid theory.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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