Abstract: Freeness is an interesting algebraic property of complex hyperplane arrangements. The standard examples of free arrangements are the Coxeter arrangements, which consist of the hyperplanes normal to the elements of a finite root system. It is a natural (open) question to determine when a subarrangement of a Coxeter arrangement is free. Surprisingly, for the inversion subarrangements this question seems to be closely connected to the combinatorics of Coxeter groups and Schubert varieties. I will talk about two aspects of this connection: (1) the equality between the exponents of a rationally smooth Schubert variety and the exponents of the corresponding inversion arrangement, and (2) a criterion for freeness of inversion arrangements using root-system pattern avoidance.