The McKay correspondence in higher dimensions
The McKay correspondence is a surprising, and beautiful, bijection (defined geometrically by du Val, and algebraically by McKay) between the isomorphism classes of Kleinian surfaces singularities and the simply laced Dynkin diagrams. I will recall this bijection and explain how it can be used to describe the Kleinian singularities, and their resolution of singularities, as moduli spaces associated to a certain non-commutative algebra. In the final part of the talk, I will describe how this construction can be extended to describe quotient singularities in higher dimensions as moduli spaces. The talk will be totally non-technical. It is based on joint work with Alastair Craw.
Dr Gwyn Bellamy, University of Glasgow