School on Singularities in Algebraic Geometry
String Theory

July 8-17, 1999

COURSES (Detailed)

Paul Aspinwall

Singularities and String Duality

Victor Batyrev

Introduction to Toric Varieties and Mirror Symmetry

Philip Candelas

String Dualities and Toric Geometry

Le Dung-Trang

Introduction to Singularities

M.S. Narasimhan

Moduli Spaces of Vector and G-bundles over Riemann Surfaces

Miles Reid

Resolution of Quotient Singularities and McKay Correspondence

Abstract: Let G in GL(n) be a finite group acting on CC^n, and consider the quotient space X = CC^n/G and a resolution (or partial resolution) Y -> X. The question behind the McKay correspondence is to ask for a relation between the geometry of Y and the group representation theory of G. For G in SL(2) and SL(3), and Y a minimal (or "crepant") resolution Y, this can be done in some detail in several quite different ways. The lectures will describe quotient singularities and their resolution, the background to McKay correspondence, several of the known approaches to proving the McKay correspondence, and many open problems arising.

Approximate program for the lectures: