 Date
 November 20^{th}  November 26^{th}, 2011
 Organizers
 Igor Burban, Bonn
 Yuriy Drozd, Kiev
 GertMartin Greuel, Kaiserslautern
 ID
 1147b
 Programme
The study of maximal CohenMacaulay modules over Noetherian local
rings has its origin in the theory of integral representations of finite groups. It grew up
from a very classical problem of classification of crystallographic groups,
related with Hilbert's 18th problem.
One of the most spectacular applications of the theory of CohenMacaulay
modules is a conceptual explanation of the socalled McKay correspondence
for finite subgroups
of SL(2, C), due to Artin, Auslander, Esnault, GonzalezSprinberg, Knörrer, Verdier
and many others.
A detailed discussion of these results is going to be one of the central aims
of this school.
We are going to focus on the following subjects.
 CohenMacaulay modules over surface singularities and the McKay
correspondence for the quotient surface singularities.

Vector bundles on genus one curves, Kahn's functor and the geometric McKay correspondence
for the minimally elliptic surface singularities.
 CohenMacaulay modules over degenerate cusps.

Geometry of normal surface singularities.
 Preparatory reading


W. Bruns, J. Herzog, CohenMacaulay rings,
Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1993.
 I. Burban, Yu. Drozd, Maximal CohenMacaulay modules over surface singularities,
in Trends in representation theory of algebras and related topics, 101166, 2008.
 J.P. Serre, Local Algebra, Springer Monographs in Mathematics, 2000.
 Yu. Yoshino, CohenMacaulay modules over CohenMacaulay rings, LMS Lecture Note Series, 146. Cambridge University Press, Cambridge, 1990.
 References on vector bundles on genus one curves and CohenMacaulay modules over minimally elliptic singularities
and their degenerations

 L. Bodnarchuk, I. Burban, Yu. Drozd, G.M. Greuel,
Vector bundles and torsion free sheaves on degenerations of elliptic curves,
in
Global aspects of complex geometry, 83128, Springer, 2006.
 I. Burban, Yu. Drozd,
Maximal CohenMacaulay modules over nonisolated surface singularities,
arXiv:1002.3042.
 Yu. Drozd, Vector bundles and CohenMacaulay modules, in Representations of finite dimensional algebras and related topics in Lie theory and geometry, 189222, Fields Inst. Communications
40, 2004.

C. Kahn, Reflexive modules on minimally elliptic singularities,
Math. Ann. 285 (1989), no. 1, 141160.
 Deadline for applications
 15 September 2011
The seminars take place at the
Mathematisches Forschungsinstitut Oberwolfach.
The number of participants is restricted to 25.
The Institute covers accommodation and food.
We are pleased that the Carl Friedrich von Siemens Foundation has decided
to support the Oberwolfach Seminars from summer 2008 to summer 2013.
By this support, travel expenses can be reimbursed up to 200 Euro in average per person.
Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts.
Applications including
 full name and address, including email address
 present position, university
 name of supervisor of Ph.D. thesis
 a short summary of previous work and interest
should be sent preferably by email (.ps or .pdf file) to:
Prof. Dr. Dr. h.c. GertMartin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
Mathematisches Forschungsinstitut Oberwolfach
updated: April 20 ^{th}, 2011