Collaborative Research Centers and Transregios

SFB 647: Space - Time - Matter. Analytic and Geometric Structures

Mathematicians and physicists work jointly in the SFB 647 to find interdisciplinary solutions for questions that arise roughly from two major fields. First, there is the geometry of matter. In this field we investigate the composition and classification of special geometric structures that are relevant for quantum field theory, string theory and cosmology. Second, we analyze the evolution of geometric structures. This comprises special solutions, deformations, singularity constructions and properties of stability for relevant partial differential equations.

CRC/TRR 109: Discretization in Geometry and Dynamics

The CRC/Transregio pursues research on the discretization of differential geometry and dynamics. In both fields of mathematics, the objects under investigation are usually governed by differential equations. The common idea is to find and investigate discrete models that exhibit properties and structures characteristic of the corresponding smooth geometric objects and dynamical processes. The resulting discretization constitutes a fundamental mathematical theory, which incorporates the classical analog in the continuous limit.

CRC 1114: Scaling Cascades in Complex Systems

Complex processes with scaling cascades define a large number of natural scientific systems. Their simulation remains a major challenge due to the very large number of degrees of freedom and cross-scale interactions. The CRC "Scaling Cascades in Complex Systems" seeks to develop adequate modeling techniques, by means of which the target variables of the respective simulation can be calculated efficiently. To achieve this, it brings mathematics researchers together with colleagues in biochemistry, physics and earth sciences, who are jointly working on consolidating methodological developments for the modeling and simulation of complex processes with scaling cascades and thus advancing answers to prototypical natural scientific issues.

CRC TRR 154: Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks

The successful energy transition is of huge public interest. It is also of major significance in socially, politically and economically terms. As many other industrial nations, Germany relies dramatically on a solid, secure, efficient and affordable energy supply. Within the next decades gas as a source of energy will play a crucial role – not only in light of the nuclear phase-out. The TRR 154 is aiming to find solutions to these challenges by means of mathematical modeling, simulation and optimization and hence offering new standards of quality.