Finite-orbit compactifications of additive groups associated to subspace arrangements

Recent advances in combinatorics have been enabled by the study of "matroid Schubert varieties", a kind of finite-orbit compactification of $\mathbb{G}_a^n$ that arises from hyperplane arrangements. We will theory of these varieties, then discuss a recent generalization to subspace arrangements. This work is joint with Colin Crowley & Botong Wang.