McKay Correspondence (Summer Semester 2014)

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  • Place and Time: Tu 12-14 and Th 14-16 in Room 218, Eckerstr 1.
  • Begins: 24.June 2014
  • Lecturer: Anda Degeratu
  • Assistent: Ming Li, Th 12-14 in Room 204, Eckerstr 1.

Course Description

The McKay Correspondence establishes a correspondence between the finite subgroups of SL(2, C) and the ADE type Dynkin diagrams. It has important consequences in understanding the geometry and topology of minimal resolutions of rational double points, from where it ramifies itself into a plethora of directions (like algebraic geometry, complex geometry and manifolds with special holonomy, representation theory) which will be investigated in this course.


  • McKay: Graph, singularities, and finite groups, 1979
  • Slodowy: Simple singularities and simple algebraic groups, 1980
  • Gonzalez-Sprinberg and Verdier: La correspondence de McKay, 1989
  • Kronheimer: The construction of ALE spaces as hyperkähler quotients, 1989
  • Kronheimer and Nakajima: Yang-Mills instantons on ALE gravitational instantons, 1990
  • Ito and Reid: The McKay correspondence for finite subgroups of SL(3,C), 1998
  • Bridgeland, King, and Reid: The McKay correspondece as an equivalence of derived categories, 2001
  • Joyce: Compact manifolds with special holonomy, 2000

Tentative Program

  • Week 1: Overview; Representation theory of finite subgroups of SL(2,C); the McKay Correspondence
  • Week 2: Minimal resolutions of rational double points; the work of Gonzalez-Sprinberg and Verdier
  • Week 3: the work of Kronheimer and of Kronheimer and Nakajima
  • Week 4: Higher dimensional McKay Correspondence, crepant resolutions
  • Week 5: the result of Bridgeland, King, and Reid
  • Week 6: special holonomy, current results.
Last update: 2014-06-23 14:55:26.