De Loera's Ehrhart positivity and unimodality conjecture for matroid polytopes

Let $M$ be a matroid, and let $\mathscr{P}(M)$ denote its matroid polytope. The $h^*$-polynomial of $\mathscr{P}(M)$ is the polynomial whose coefficient vector is being considered. De Loera's conjecture. The Ehrhart polynomial of every matroid polytope has positive coefficients, and the vector of coefficients of the $h^*$-polynomial is unimodal.

De Loera et al. posed this conjecture based on computational evidence. The positivity assertion has further supporting results, including positivity for matroid polytopes of uniform matroids, while the full statement remains open in the supplied context.