Abstract:Given an affine hyperplane arrangement with some additional structure, we define two finite dimensional noncommutative algebras, both of which are motivated by the geometry of a corresponding hypertoric variety. We show that these algebras are Koszul dual to one another, and that the roles of the two algebras is reversed by Gale duality of Hyperplane arrangements. This is joint work with Tom Braden, Nick Proudfoot, and Ben Webster.