Intersection cohomology of symplectic implosions

Symplectic implosion is an abelianisation construction in symplectic geometry. The implosion of the cotangent bundle of a group K plays a universal role in the implosion of manifolds with a K-action.  This universal implosion, which is usually a singular variety, can also be viewed as the non-reductive Geometric Invariant Theory quotient of the complexification G of K by its maximal unipotent subgroup. 

In this talk, we describe joint work with Johan Martens and Nick Proudfoot which uses point-counting techniques to calculate the intersection cohomology of the universal implosion.