Chow rings of matroids are Koszul

Abstract: Koszul algebras have long been studied in connection with topology and representation theory for their exceptional homological and duality properties, and they appear with incredible frequency among rings at the intersection of commutative algebra, algebraic geometry, and combinatorics. The Chow ring of a matroid is just such a ring - a commutative, graded, Artinian, Gorenstein algebra with linear and quadratic relations defined by the matroid, which recently played an important role in establishing a number of long-standing conjectures on the combinatorics of matroids.

In this talk, I will discuss joint work with Jason McCullough affirmatively answering a conjecture of Dotsenko that the Chow ring of any matroid is Koszul. Time permitting, I will also mention some potential implications of this fact. No prior experience with matroids is necessary for the talk.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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