### Speaker

Alastair Craw
(Bath)

### Description

For a positive integer n and a finite subgroup \Gamma in SL(2,C), I’ll describe work in preparation with Ryo Yamagishi which shows that the Hilbert scheme of n-points on C^2/\Gamma is reduced. In fact, it’s isomorphic to a Nakajima quiver variety, so it has symplectic singularities and it admits a unique crepant resolution. This strengthens previous joint work of mine with Gammelgaard, Gyenge and Szendroi. The main tool is a generalisation of the Le Bruyn-Procesi theorem which describes the invariant algebra for the natural action of the product of general linear groups on the space of representations of a quiver for a given dimension vector.