Minicourse: The McKay Correspondence

The McKay correspondence is an amazing correspondence between finite subgroups of SL(2,C) and the geometry of the resolution of certain singularities. Understanding why this correspondence works and generalizing it to SL(n,C) has inspired many interesting ideas in recent years. This minicourse will decribe the correspondence in detail and introduce some of the mathematics required to understand how to generalize it. I will try to make this course accessible to people who know little algebraic geometry. The McKay correspondence is intertwined with many ideas in string theory but I will probably not cover this.