We introduce certain torus-equivariant classes on permutohedral varieties which we call
“tautological classes of matroids” as a new geometric framework for studying matroids …

We introduce a presentation of the Chow ring of a matroid by a new set of generators, called
“simplicial generators.” These generators are analogous to nef divisors on projective toric …

This article is an introduction to matroid theory aimed at algebraic geometers. Matroids are
combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all …

We study the maximum likelihood (ML) degree of linear concentration models in algebraic
statistics. We relate it to an intersection problem on the variety of complete quadrics. This …

Matroid theory is a combinatorial theory of independence which has its origins in linear
algebra and graph theory and turns out to have deep connections with many other fields …

In 1982, Demailly showed that the Hodge conjecture follows from the statement that all
positive closed currents with rational cohomology class can be approximated by positive …

For any matroid M, we compute the Tutte polynomial TM (x, y) using the mixed intersection
numbers of certain classes in the combinatorial Chow ring A∙(M) arising from …

Given a root system Φ of type A n, B n, C n, or D n in Euclidean space E, let W be the
associated Weyl group. For a point p∈ E not orthogonal to any of the roots in Φ, we consider …

The equivariant Ehrhart theory of the permutahedron Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 148, Number 12, December 2020, Pages …

The closure of a generic torus orbit in the flag variety G/B of type A n− 1 is known to be a
permutohedral variety and well studied. In this paper we introduce the notion of a generic …