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

In a recent paper, the first author proved the log-concavity of the coefficients of the
characteristic polynomial of a matroid realizable over a field of characteristic 0, answering a …

We construct an intersection product on tropical cycles contained in the Bergman fan of a
matroid. To do this we first establish a connection between the operations of deletion and …

We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to
algebraic intersection points with expected multiplicities, provided that the tropicalizations …

In this paper we use the connections between tropical algebraic geometry and rigid-analytic
geometry in order to prove two main results. We use tropical methods to prove a theorem …

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

This paper is the first in a series devoted to the development of a Hodge theory for tropical
varieties. We introduce a notion of T-stability for tropical fans and prove that various …

The aim of this paper is to study homological properties of tropical fans and to propose a
notion of smoothness in tropical geometry, which goes beyond matroids and their Bergman …

We show how to equip the cone complexes of toroidal embeddings with additional structure
that allows to define a balancing condition for weighted subcomplexes. We then proceed to …

Abstract Chambert-Loir and Ducros have recently introduced a theory of real valued
differential forms and currents on Berkovich spaces. In analogy to the theory of forms with …