Syzygies of hyperplane arrangements and matroids

We present an explicit combinatorial construction for the minimal free resolutions of the ideals arising from hyperplane arrangements and matroids. This "lifts" Stanley's formula for the Betti numbers of such ideals. Connections to hyperplane arrangements on a torus are explored. A relationship is given between graphic and co-graphic arrangements, Tutte dichromatic polynomials, and Hermite orthogonal polynomials. This is a joint work with Isabella Novik and Bernd Sturmfels.