(Rational) homotopy groups from matroids

A complex hyperplane arrangement can be regarded as a realization of a (simple) matroid. Accordingly, many (but not all) topological invariants of the complement of the hyperplane arrangement can be described in terms of the combinatorics of the matroid. I will describe recent work with Alex Suciu that continues this theme by introducing combinatorially-defined "higher homotopy groups" of arbitrary matroids that agree with (rational) homotopy groups of hyperplane complements in certain cases.