Algebraic Geometry Seminar

The McKay Correspondence: Motivic Integration and Derived Categories

Alastair Craw, Utah

Abstract

By associating a graph to each finite subgroup G of SL(2,C), John McKay uncovered a beautiful

link between representations of G and geometrical properties of the minimal resolution

of the quotient C2/G. I?ll discuss two generalisations of this result to higher dimensions:

Kontsevich?s theory of motivic integration, and the Fourier-Mukai transform approach of

Bridgeland, King and Reid. If time permits I?ll discuss recent work on finding a link between

the two approaches.