As any matroid theorist will enthusiastically tell you, matroids exhibit many strong and subtle relationships with other areas of mathematics. The past two decades have brought a resurgence of interest in matroid theory, with a crowning jewel being the positive solution of Mason's conjecture in 2018 (by two independent groups). To the surprise of many, one proof of this result uses deep tools from algebraic geometry. We provide an introduction to the theory of matroids through graph theory and polyhedral geometry before building toward some deep connections with algebraic geometry which were used in the proof. In particular, we will see that modern matroid theory benefits from relations with the geometry of toric varieties, intersection theory, and Hodge theory.
Zoom Link: https://washington.zoom.us/j/92849568892