General philosophy

We aim at a comprehensive teaching and research program based on geometric, algebraic, stochastic, and analytic approaches, complemented by efficient numerical and computational implementations. We want that our fellows succeed in qualifying as a part of the next generation of leading scientists in academia or industry. We designed the research and study program for you. The most important aspect, however, is that we also count on you to shape this program and fill it with life. Whatever is good for your PhD and your career, is almost certainly also good for the research training group as a whole, so we are going to support it. We want you to get well connected with the leading scientists in your field, to gain international visibility, and to learn all you need to achieve your goals. One feature of how we want to support this is by embedding your research into the structured PhD program, allowing for interaction with the other fellows, but avoiding to take too much of your time away. We also strive to provide two Principal Investigators (PIs) as advisors, and whenever possible one postdoc as an additional mentor. The doctoral students benefit from having a young researcher as further consultant who will provide research advice. However, the role of the mentors goes beyond mere assistance in scientific work. They also help the doctoral students to overcome various individual problems arising from entering a new living situation and facing the demands of internationally competitive scientific work. On the other hand, the mentors have the opportunity to gain practical experience in promoting junior scientists, which helps them in the future when they form their own research teams.

Research Philosophy

The unique profile of the RTG is based on complexity aspects in different mathematical settings, and on different methodologies to cope with this complexity. Most of our research areas "export" and "import" complexity reduction methodology, i.e., they produce new approaches that are helpful in other CoRe areas, and they profit from advanced insights themselves. This yields highly welcome multi-way interactions in the research program.

Teaching Philosophy

The ambitious goal of the RTG is to provide a comprehensive training in mathematical complexity reduction. We want to incorporate ideas and knowledge from many different mathematical subdisciplines. One important component of our study program are four fundamental compact (one week) courses, especially designed for the RTG and taught in English language. They provide the doctoral students with a broad knowledge of state-of-the-art methods in the various subdisciplines of complexity reduction. The students can complement their know- how and the courses also provide a platform for exchange of knowledge. Every student in the RTG (also the associated ones) has to attend each of the four courses once. The courses are jointly designed and taught by the PIs, specifically for the RTG. To further encourage early integration into the scientific community and networking they will actively participate in the weekly seminar.