Simplicial generation of Chow rings of matroids
Matroids are combinatorial objects that capture the essence of linear algebra. We give a gentle introduction to the recent breakthrough in matroid theory via an algebro-geometric approach, a.k.a. the Hodge theory of matroids by Adiprasito, Huh, and Katz. We will then show how to push the geometry and combinatorics further to give a simplified proof the main portion of the Hodge theory of matroids. This is joint work with Spencer Backman and Connor Simpson.