The Heron-Rota-Welsh Conjecture for matroids representable over ℂ

Matroid theory originated in 1935 with the works of Hassler Whitney, whose objective was to construct a combinatorial object that captured the abstract properties of dependence that are common to linear algebra and graph theory. In the 1970s, Heron and Rota conjectured that the absolute values of the coefficients of the characteristic polynomial of a matroid (the so-called Whitney's numbers of the first kind) are unimodal, and Welsh later conjectured that they are log-concave. The conjecture asserting the log-concavity and unimodality of the Whitney's numbers of the first kind for any matroid is known as the Heron-Rota-Welsh Conjecture. The concept of the Chow ring of a matroid originated in 2004 through the work of Feichtner and Yuzvinsky, who defined it as a generalization of the cohomology ring of the wonderful model of an arrangement of subspaces. The construction of the wonderful model itself was first established in 1996 by De Concini and Procesi. The Heron-Rota-Welsh conjecture was proved in 2018 by Karim Adiprasito, June Huh, and Eric Katz. The key innovation in their proof was establishing the Kähler package for the Chow ring of a matroid.