Project Details
Projekt
GRK 1269: Global Structures in Geometry and Analysis
Subject Area
Mathematics
Term
from 2006 to 2015
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 968940
Manifolds are geometric spaces, which are described by systems of non-linear equations. They appear in almost all fields of mathematics and its applications, e.g. as phase or model spaces in physics and applied mathematics, as minimal surfaces and spaces with certain curvature properties in differential geometry, or as modular varieties in number theory. The manifolds encountered in practice will always carry an additional global structure that encodes information about the context in which they were defined. For instance, the phase spaces of mechanics or optics carry a symplectic or a contact structure, twistor spaces over certain Riemannian manifolds are complex and uniruled.
Although these spaces and their global structures are classically studied in different fields of mathematics, it is today no longer possible to restrict oneself to methods of one discipline alone; much of the last decade's progress was gained through collaboration of mathematicians from various fields. Accordingly, our research programme, whose projects are mostly located between the classical branches of mathematics, combines the competences of mathematicians working in three different fields for the study of global structures. We aim to classify manifolds with special geometric structures and study invariants that help to divide manifolds into several classes. We also study moduli spaces and develop methods to construct new examples of manifolds with special structures.
Our study programme has a similar interdisciplinary approach. We have introduced a number of interdisciplinary research seminars and courses. Supervision of PhD students by two advisors from different fields is the norm. The most important feature of our study programme, however, is its strong international component. Among other means, research travels to our cooperation partners and our workshop programme guarantee that our PhD students are embedded into the international scientific community right from the beginning. The students will also benefit from a large number of cooperations with other research institutions and programmes in the area, in particular the Transregional Collaborative Research Centre 12.
Although these spaces and their global structures are classically studied in different fields of mathematics, it is today no longer possible to restrict oneself to methods of one discipline alone; much of the last decade's progress was gained through collaboration of mathematicians from various fields. Accordingly, our research programme, whose projects are mostly located between the classical branches of mathematics, combines the competences of mathematicians working in three different fields for the study of global structures. We aim to classify manifolds with special geometric structures and study invariants that help to divide manifolds into several classes. We also study moduli spaces and develop methods to construct new examples of manifolds with special structures.
Our study programme has a similar interdisciplinary approach. We have introduced a number of interdisciplinary research seminars and courses. Supervision of PhD students by two advisors from different fields is the norm. The most important feature of our study programme, however, is its strong international component. Among other means, research travels to our cooperation partners and our workshop programme guarantee that our PhD students are embedded into the international scientific community right from the beginning. The students will also benefit from a large number of cooperations with other research institutions and programmes in the area, in particular the Transregional Collaborative Research Centre 12.
DFG Programme
Research Training Groups
Applicant Institution
Universität zu Köln
Spokesperson
Professor Dr. Guido Sweers
