GRK 2297:  Mathematical Complexity Reduction (CoRe)

• Subject Area: Mathematics
• Term: since 2017
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 314838170

In the context of the proposed RTG we understand complexity as an intrinsic property that makes it difficult to determine an appropriate mathematical representation of a real world problem, to assess the fundamental structures and properties of mathematical objects, and to algorithmically solve a given mathematical problem. By complexity reduction we refer to all approaches that help to overcome these difficulties m a systematic way and to achieve the aforementioned goals more efficiently. For many mathematical tasks, approximation and dimension reduction are the most important tools to obtain a simpler representation and computational speedups. We see complexity reduction in a more general way and also investigate, e.g., liftings to higher-dimensional spaces and consider the costs of data observation. Our research goals are the development of cross-disciplinary mathematical theory and methods for complexity reduction and the identification of relevant problem classes and effective exploitation of their structures. Our comprehensive teaching and research program is based on geometric, algebraic, stochastic, and analytic approaches, complemented by efficient numerical and computational implementations. In order to ensure the success of our doctoral students, they participate in a tailored structured study program. It contains training units in form of compact courses and weekly seminars, and encourages early integration into the scientific community and networking. The RTG has been serving as a catalyst for a dissemination of these successful practices within the Faculty of Mathematics and improving the gender situation. Complexity reduction is a fundamental aspect of the scientific backgrounds of the principal investigators. The combination of expertise from different areas of mathematics gives the RTG a unique profile, with high chances for scientific breakthroughs. The RTG is linked to two faculties, a Max Planck Institute, and several national and international research activities in different scientific communities. Our students have been trained to become proficient in a breadth of mathematical methods, and thus be ready to cope with challenging tasks in particular in cross-disciplinary research teams. We expect a continued impact both in terms of research successes, and in the education of the next generation of leading scientists in academia and industry.

• DFG Programme: Research Training Groups
• Applicant Institution: Otto-von-Guericke-Universität Magdeburg
• Spokesperson: Professor Dr. Sebastian Sager
• Participating Researchers: Professor Dr. Peter Benner; Professorin Dr. Alexandra Carpentier, until 10/2021; Professor Dr. Marc Ditzhaus, since 10/2022; Professor Dr.-Ing. Rolf Findeisen, until 10/2021; Dr. Jan Heiland, until 9/2024; Professorin Dr. Anja Janßen; Professor Dr. Thomas Kahle; Professor Dr. Volker Kaibel; Professorin Dr. Claudia Kirch; Professor Dr. Maximilian Merkert, until 10/2021; Professor Dr. Benjamin Nill, from 4/2017 until 9/2021; Dr. Feliks Nüske, since 10/2022; Professor Dr. Thomas Richter; Professorin Dr. Petra Nora Schwer, until 9/2024