Third-party funded projects
In addition to the overarching Hausdorff Center for Mathematics, the department hosts or participates in a number of third party funded research and training projects on specific mathematical topics.
- Collaborative Research Center (SFB) 1060 'The Mathematics of Emergent Effects'
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This project is funded by the German Research Foundation (DFG). Bonn is the host university of SFB 1060.
The central aim of the Cooperative Research Center (SFB) is to understand the emergence of new effects at larger scales from the interaction of many units at a smaller scale. The SFB will dvelop new rigorous mathematical concepts and tools to address this phenomenon and sharpen and test these tools in specific situations. The SFB focuses on three interrelated themes, which are reflected by the following Project Groups:
- From quantum mechanics to condensed matter and materials science
- Stochastic systems and contiuum limits
- Geometric structures and high dimensional problems
The SFB builds on existing strong synergies between analysis, stochastics and numerics at Bonn. The SFB will systematically exploit new interactions in particular beween analysis and statistical mechanics, through differnt aspects of random matrix theory, in the interplay of new geometric description and efficient computation, and using complementary points of view in many-body quantum mechanics.
- Collaborative Research Center (SFB) - Transregio 45 'Periods, moduli spaces and arithmetic of algebraic varieties' Bonn – Mainz – Essen
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This project is funded by the German Research Foundation (DFG). Bonn participates in SFB/TR 45.
The SFB/TR has its focus on research about Periods, Moduli Spaces and related aspects of the Arithmetic of Algebraic Varieties. These are very active research areas, directed towards central questions in the theory of algebraic varieties. Some of the most exciting developments take place where arithmetic and geometry meet, and where one is looking for new methods, building yet unknown bridges between different points of view. Many of the algebraic varieties studied in our projects are relevant to other sciences like mathematical physics or computer science.
- Research Training Group (GRK) 1150 'Homotopy and Cohomology'
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This project is funded by the German Research Foundation (DFG).
Topology stands out amongst other branches of mathematics for the way it bridges the gap between the realm of continuous phenomena (geometry and analysis) and the discrete world (algebra and combinatorics). Topology uses discrete techniques to study continuous objects; it has assimilated methods from many areas of mathematics, and methods developed by topologists have in turn contributed significantly to advances in other areas.
Recent new theories and methods will provide the thesis topics in the proposed Research Training Group. To be more specific, we will concentrate on the following themes: Classifying spaces and cohomology of groups, Configuration spaces and mapping spaces, Moduli spaces, Stable homotopy theory, Elliptic cohomology and topological modular forms, Operads and E-infinity structures, Manifolds and bordism theory, Cohomology and homotopy theory of foliations.
- International Max Planck Research School (IMPRS) 'Moduli Spaces'
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This project is funded by the Max Planck Society (MPG).
The IMPRS for Moduli Spaces is a joint project of the Max Planck Institute for Mathematics and the University of Bonn. It is an extension of the Bonn International Graduate School in Mathematics in the specific research direction of moduli spaces. The IMPRS is sponsored by the Max Planck Society.
Mathematical objects of a given type often come in families depending on continuous parameters. These parameters are generally called moduli. So in a sense there are as many moduli spaces as types of mathematical objects, and for this reason moduli spaces form a cross-section of many domains of mathematics.
Very surprisingly, moduli spaces (e.g., of vector bundles, of stable maps, etc.) were discovered in recent years to play an important role in mathematical physics, especially in the theory of quantum strings, which strives to the unification of quantum field theory and the theory of gravity.
- Further projects
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A selection of further research projects in which Bonn participates:
- DFG Priority Program 1253: Optimization with partial differential equations
- DFG Priority Program 1388: Representation theory
- DFG Priority Program 1590: Probabilistic Structures in Evolution
- DFG Research Unit 797: Analysis and computation of microstructure in finite plasticity
