Hypertoric varieties -- Nicholas Proudfoot.

A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics of hyperplane arrangements and matroids. I will give an introduction to these spaces, and use arithmetic techniques to obtain combinatorial interpretations of the Betti numbers of hypertoric varieties, both for ordinary cohomology in the smooth case and intersection cohomology in the singular case.