The classification of hypertoric varieties

Hypertoric varieties are conical symplectic singularities equipped with a hamiltonian action of a torus of maximal possible dimension. They behave analogously to toric varieties in many ways, with the hamiltonian torus replacing the dense torus. Examples include: (crepant partial resolutions of) rational surface singularities of type A, the cotangent bundle of projective space, and Nakajima quiver varieties with the `all 1s' dimension vector.

Arbo and Proudfoot conjectured a combinatorial classification of hypertoric varieties by zonotopal tilings. In this talk I will discuss a proof of the conjecture.