**Date:**- October 9th - October 15th, 2005
**Organizers:**- Ragnar-Olaf Buchweitz, Toronto
- Hubert Flenner, Bochum
**Programme:**-
It was Riemann's insight that smooth compact complex
curves of fixed genus g depend on 3g-3 complex
parameters, which he determined in an elegant and simple
manner via coverings of the projective line. Ground breaking
work in deformation theory of higher dimensional complex
manifolds was done by Kodaira and Spencer in the late 50s
of the last century. They introduced the concept of a "versal
deformation", which in a certain sense is a local moduli
space. In its beginnings, this theory was basically concerned
with variations of complex structures on a given complex
manifold, and the theory of elliptic differential operators
played a central role. Using ideas of Grothendieck, modern deformation
theory was soon formalized, and, as a consequence, gained
a much wider range of application, e.g., on singularities,
vector bundles, and modules.
As a side effect of its formalization, modern deformation theory is difficult to access for the beginner. The seminar aims to give an introduction oriented towards the practical user's needs, so that the methods of deformation theory can become tools for concrete problems in complex analytic and algebraic geometry. Among other things, the following items will be treated: formal deformation theory, versal and semi-universal deformation, criteria for smoothness and unobstructedness of the base space of a versal deformation, determination of the components of the semi-universal deformation, openness of versality, moduli spaces, cotangent complexes. The theory will be presented in connection with application examples such as compact spaces, modules and singularities.

**Prerequisites:**- Solid knowledge in complex analytic or algebraic geometry, sheaf theory and cohomology theory.
**Deadline for applications:**- September 1st, 2005
- The seminars take place at the
Mathematisches Forschungsinstitut Oberwolfach.
The number of participants is restricted to 24.
The Institute covers accommodation and food.
Travel expenses cannot be reimbursed.
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 as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel

Universität Kaiserslautern

Fachbereich Mathematik

Erwin Schrödingerstr.

67663 Kaiserslautern, Germany

.

Mathematisches Forschungsinstitut Oberwolfach updated: January 7th, 2005