Nicholas Proudfoot: Orlik–Terao algebras and internal zonotopal algebras

Abstract: I’ll begin by considering two different algebras that admit actions of the symmetric group. The first is the cohomology ring of a certain configuration space, and the second is the intersection cohomology of a hypertoric variety. (Explicit presentations of the rings will be given, so anyone can feel free to ignore the topology if they want.) Although these are not isomorphic as rings, Pagaria proved that they are isomorphic as graded representations of the symmetric group. I’ll outline a proof of a more general statement about arbitrary hyperplane arrangements, and explain that Pagaria’s theorem can be obtained by specializing to the case of the Type A Coxeter arrangement. This is based on joint work with Colin Crowley.