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

We show that the mesh mutations are the minimal relations among the gg‐vectors with
respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result …

Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids
are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the partial …

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 …

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 …

We initiate the study of a class of polytopes, which we coin polypositroids, defined to be
those polytopes that are simultaneously generalized permutohedra (or polymatroids) and …

We study valuated matroids, their tropical incidence relations, flag matroids, and total
positivity. This leads to a characterization of permutahedral subdivisions, namely …

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 …

For any lattice congruence of the weak order on permutations, Reading proved that gluing
together the cones of the braid fan that belong to the same congruence class defines a …