McKay Correspondence (Summer Semester 2014)
- 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.
Bibliography
- 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.
