Intersection cohomology and quantum cohomology of conical symplectic   resolutions
  For any conical symplectic resolution, we give a conjecture relating the intersection cohomology of the singular cone to the quantum cohomology of its resolution. We prove this conjecture for hypertoric varieties, recovering the ring structure on hypertoric intersection cohomology that was originally constructed by Braden and the second author. 
Michael McBreen and Nicholas Proudfoot
math.AG