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

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The
decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem …

I will tell two interrelated stories illustrating fruitful interactions between combinatorics and
Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter …

Polymatroids are combinatorial abstractions of subspace arrangements in the same way that
matroids are combinatorial abstractions of hyperplane arrangements. By introducing …

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 …

We establish a connection between the algebraic geometry of the type BB permutohedral
toric variety and the combinatorics of delta‐matroids. Using this connection, we compute the …

In this article, we make several contributions of independent interest. First, we introduce the
notion of stressed hyperplane of a matroid, essentially a type of cyclic flat that permits to …

We study the K-ring of the wonderful variety of a hyperplane arrangement and give a
combinatorial presentation that depends only on the underlying matroid. We use this …