The study of maximal Cohen-Macaulay 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 18-th problem. One of the most spectacular applications of the theory of Cohen-Macaulay modules is a conceptual explanation of the so-called McKay correspondence for finite subgroups of SL(2, C), due to Artin, Auslander, Esnault, Gonzalez-Sprinberg, 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.
- Cohen-Macaulay 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.
- Cohen-Macaulay modules over degenerate cusps.
- Geometry of normal surface singularities.
- W. Bruns, J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1993.
- I. Burban, Yu. Drozd, Maximal Cohen-Macaulay modules over surface singularities, in Trends in representation theory of algebras and related topics, 101-166, 2008.
- J.-P. Serre, Local Algebra, Springer Monographs in Mathematics, 2000.
- Yu. Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings, LMS Lecture Note Series, 146. Cambridge University Press, Cambridge, 1990.
- 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, 83-128, Springer, 2006.
- I. Burban, Yu. Drozd, Maximal Cohen-Macaulay modules over non-isolated surface singularities, arXiv:1002.3042.
- Yu. Drozd, Vector bundles and Cohen-Macaulay modules, in Representations of finite dimensional algebras and related topics in Lie theory and geometry, 189-222, Fields Inst. Communications 40, 2004.
- C. Kahn, Reflexive modules on minimally elliptic singularities, Math. Ann. 285 (1989), no. 1, 141-160.
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 e-mail address
- present position, university
- name of supervisor of Ph.D. thesis
- a short summary of previous work and interest
should be sent preferably by e-mail (.ps or .pdf file) to:
Prof. Dr. Dr. h.c. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany