We introduce the conormal fan of a matroid $\operatorname {M} $, which is a Lagrangian
analog of the Bergman fan of $\operatorname {M} $. We use the conormal fan to give a …

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 …

This article provides a comprehensive exposition about inequalities that the coefficients of
Ehrhart polynomials and h-polynomials satisfy under various assumptions. We pay …

We prove that the number of tropical critical points of an affine matroid is equal to the beta
invariant of. Motivated by the computation of maximum likelihood degrees, this number is …

The harmonic polytope and the bipermutahedron are two related polytopes which arose in
Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We study the …

We establish faithful tropicalisation for point configurations on algebraic tori. Building on
ideas from enumerative geometry, we introduce tropical scaffolds and use them to construct …

We prove that the maximum likelihood degree of a matroid M equals its beta invariant. For
an element e of M that is neither a loop nor a coloop, this is defined to be the degree of the …

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 …