We study the class of Lorentzian polynomials. The class contains homogeneous stable
polynomials as well as volume polynomials of convex bodies and projective varieties. We …

We study an operation in matroid theory that allows one to transition a given matroid into
another with more bases via relaxing a stressed subset. This framework provides a new …

We study the Hilbert series of four objects arising in the Chow-theoretic and Kazhdan–
Lusztig framework of matroids. These are, respectively, the Hilbert series of the Chow ring …

Describing the equality conditions of the Alexandrov–Fenchel inequality has been a major
open problem for decades. We prove that for a natural class of convex polytopes, the …

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 …

A long-standing conjecture due to R. Fox states that the coefficients of the Alexander
polynomial of an alternating knot exhibit a trapezoidal pattern. In other words, these …

For several classical nonnegative integer functions we investigate if they are members of the
counting complexity class# P or not. We prove# P membership in surprising cases, and in …

The theory of matroids or combinatorial geometries originated in linear algebra and graph
theory, and has deep connections with many other areas, including field theory, matching …

The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical
isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The …

We study combinatorial inequalities for various classes of set systems: matroids,
polymatroids, poset antimatroids, and interval greedoids. We prove log-concavity …