I will state and comment Kronheimer's Theorem on the existence of ALE hyperkaehler metrics on resolutions of SU(2)-singularities. The process will include:

outline of moment map, kahler and hyperkahler reduction, geometric motivation (yet another one!) for being interested in such things, wild speculation (simply based on the only known example) of what Nakajima examples could look like (sometimes).

This will be a particularly informal seminar!