Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Simplicial generation of Chow rings of matroids

Seminar | October 1 | 5-6 p.m. | 939 Evans Hall

 Chris Eur, UC Berkeley

 Department of Mathematics

Matroids are combinatorial objects that capture the essence of linear independence. A recent breakthrough in matroid theory is the development of Hodge theory of matroids by Adiprasito, Huh, and Katz, afforded by tools from tropical geometry. Meanwhile, matroids have also been studied as type A objects through the lens of Lie/Coxeter combinatorics. How do these two perspectives, tropical and Lie/Coxeter, relate to each other? We give an answer via a new presentation of the Chow ring of a matroid whose variables now admit a combinatorial interpretation as matroid quotients and display behaviors analogous to those of nef classes on smooth projective varieties. We discuss various applications, including the recovery of the Hodge theory of matroids. This is joint work with Spencer Backman and Connor Simpson.