Student Algebraic Geometry: The Mckay Correspondence

The Mckay Correspondence is a bijection between finite subgroups of SL(2,C), rational double points on surfaces, and the ADE Dynkin diagrams. This links various "exceptional objects" appearing in classifications, for example, associating the regular icosahedron to the E8 diagram. I will outline an explanation of the correspondence by relating the geometry of the minimal resolution of the quotient C^2/G to the representation theory of the finite subgroup G of SL(2,C). I will also mention generalizations to higher dimensions and the setting of derived categories.