Mixed volumes of matroids

This event is partially supported by PIMS.

Matroids are combinatorial objects that abstract the notion of independence. The motivating examples are matroids arising from vector configurations. An important tool for studying matroids is the associated Chow ring. A recent result of Adiprasito, Huh, and Katz is that Chow rings arising from matroids behave "nicely" in ways similar to cohomology rings of smooth projective varieties. This result has geometric inspiration, a combinatorial proof, and powerful consequences in matroid theory. In this talk, we will introduce this geometrically inspired approach to matroid theory. Then, we will present a new computation for the "mixed volume of a matroid", that is, the matroid analog to the integration map on smooth projective varieties. This is joint work with Andy Hsiao, and Kalle Karu.