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 use the geometry of the stellahedral toric variety to study matroids. We identify the
valuative group of matroids with the cohomology ring of the stellahedral toric variety and …

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 show that the modified log-Sobolev constant for a natural Markov chain which converges
to an r-homogeneous strongly log-concave distribution is at least 1/r. Applications include an …

We give a self-contained proof of the strongest version of Mason's conjecture, namely that
for any matroid the sequence of the number of independent sets of given sizes is ultra log …

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 …

We give elementary self-contained proofs of the strong Mason conjecture recently proved by
Anari et al.(2018) and Brändén and Huh (2020), and of the classical Alexandrov–Fenchel …

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

We study (unrooted) random forests on a graph where the probability of a forest is
multiplicatively weighted by a parameter β> 0 β> 0 per edge. This is called the arboreal gas …

June Huh found striking connections between algebraic geometry and combinatorics,
solved central problems in combinatorics that had remained open for decades, and …