New Collaborative Research Center/Transregio at the TU Berlin approved
On May 22, 2012 the German Research Society (DFG) approved a new collaborative mathematical research center. The TU Berlin and the TU Munich as well as associated scientists in Germany and Austria received around 6 million Euros from the DFG for a funding period ending in 2016, to carry out a large-scale collaboration. The new research center, "Discretization in Geometry and Dynamics", links together researchers in Berlin, Munich, and Austria, and connects geometry with dynamical systems. The coordinator of the center is Alexander Bobenko, Professor of Geometry at TU Berlin.
The new research center will be concerned with the problem of discretization of dynamical processes and geometric structures. Both of these respective domains, the theory of dynamical systems and differential geometry, investigate smooth objects and continuous processes, which are described by so-called differential equations. The term "discretization" is used to describe procedures for converting differential equations into difference equations. In this way, continuous processes such as satellite orbits or geometric structures such as curved surfaces in space, can be analyzed and calculated with the help of computers. An example is the decomposition of a curved glass roof into flat quadrilaterals, with which the roof can be actually constructed. Another important application area is computer graphics, which operates likewise with such polyhedral surfaces.
"We need intelligent discretization, in order to adequately represent highly complex processes and structures," says Alexander Bobenko, coordinator of the research center. "We look for discrete models, which reproduce as closely as possible the important qualitative properties of a system. In this way, a fundamental mathematical theory arises. Such a theory is also important in practice, for example, when one investigates the long-term behavior of a system."
"The modeling of a glass roof is, based on the present state of the theory, comparatively simple and attainable. Other problems present us with much larger challenges," expands Jürgen Richter-Gebert, Professor of Geometry and the chief grant applicant from the TU Munich. "An example of a process which is difficult to model, is to represent accurately the motion of molecules over a long time-scale."
The participating scientists want to work out answers to specific questions in the numerous sub-projects: the project groups A (geometry) and B (dynamics) each have 9 sub-projects, in which over 20 professors with their staff will be engaged in research. Additionally, project group C (experimental mathematics) will develop interactive tools for research and educational purposes. A small public relation unit has the task, to present the research achievements for special audiences: for teachers and students in schools, but also for the press and laymen interested in mathematics. "We are dovetailing the PR activities with existing initiatives," says Günther Ziegler, Professor of Geometry, FU Berlin. In addition to his mathematical participation he is also responsible for the PR unit of the research center. "The research results and the visualization tools of the research center will not excite only scientists," Ziegler says. "They will also directly flow into the school projects and the media relations of the Munich and Berlin partners. Here the project partners have already achieved some notable preparatory work, such as software for visualization of school mathematics and beyond.
The concept for the research center was originality proposed to the DFG by the TU Berlin (with a coordinating role) and the TU Munich in fall of 2011. The presentation of the projects and consequent evaluation by the international review committee took place on March 15-16, 2012, at the TU Berlin. On May 22, 2012 the DFG announced the result of the evaluation: the proposal for the research center was judged to be "excellent". The first funding period lasts for four years, up to two further such periods can be applied for later. "With this result we can together all be proud," a pleased Bobenko observes.
"Discretization in Geometry and Dynamical Systems"
Coordinating university: Technical University Berlin, Coordinator: Professor Dr. Alexander Bobenko; further participating universities: Technical University Munich -- otherwise involved: Free University Berlin, Technical University Graz, Technical University Vienna, Austria.