Quantum Cohomology of Hypertoric Varieties

Hypertoric varieties are hyperkahler analogues of toric varieties,
obtained as the quotient of a hyperkahler vector space by a torus
action. Much like toric varieties, their geometry can be encoded in a
combinatorial way, by means of hyperplane arrangements. Smooth
hypertoric varieties are also examples of symplectic resolutions,
other examples of which include cotangent bundles to flag varieties
and Nakajima quiver varieties. These are fundamental objects in modern
representation theory and mathematical physics; in particular, their
quantum cohomology provides fruitful links between the two. In this
talk we give a complete description of the equivariant quantum
cohomology ring of hypertoric varieties in combinatorial terms. Time
permitting, I will explain potential applications for quiver
varieties. Joint work with Michael McBreen.