The Geometric Structure of Matroids

Matroids capture the common structure of independence in settings ranging from linear algebra to graph theory. Introduced independently by Hassler Whitney and Takeo Nakasawa in the 1930s, they appear naturally across mathematics and play an important role in combinatorial optimization and tropical geometry.

Recent work in matroid theory has focused on properties such as unimodality, log-concavity, and positivity of associated combinatorial sequences and polynomials. A powerful approach, rooted in work of Jack Edmonds, is to study a matroid through its base polytope. In this talk, I will introduce this geometric perspective and show how it leads to recent results on matroid invariants and matroid polytopes.