The International Research Training Group (IRTG) between Bielefeld University and Seoul National University focuses on the search for the regular in the irregular. In a truly international environment, doctoral students learn to discover and to exploit structures that help to understand singular and random systems.
Mankind has been fascinated by regular structures for a very long time. Not only scientists have tried to create or to detect regular patterns in various contexts. The world, however, is full of irregular structures, like those of cancer cells, galaxies or motion curves of microscopic particles. Scientists, especially mathematicians, have tried to uncover hidden laws which govern the generation of irregularities.
The IRTG concentrates on advanced techniques from the mathematical field of Analysis together with latest developments in neighboring fields such as Mathematical Physics, Geometry or Probability Theory. The focus is on the mathematical analysis of problems which generically exhibit singular features or randomness. The topics in which the search for the regular in the irregular is conducted include nonlinear wave equations, integro-differential equations, oscillator models, random matrices, generalized Dirichlet and magnetic energy forms, analysis on manifolds and fractal metric spaces. The initiative involves 19 internationally renowned experts from Germany and South Korea in the aforementioned fields who commit themselves to the education and the training of doctoral students coming from all over the world.
The IRTG offers a broad mathematical education on the one hand and fascinating research projects under the supervision of experts on the other hand. After having attained a solid basis through four Introductory Lectures, students work in one of the four research areas into which the research program on singular and random systems is structured. These four areas are reflected in more specialized Topics Lectures leading up to recent developments of international research. The involvement of researchers from two universities on two different continents allows the IRTG to offer a well-rounded qualification program centered around mathematical analysis. During joint workshops in 2013, 2014, and 2015 it became clear that the complementary expertise in research and education in both departments provides a unique and strong basis for the proposed initiative. During their exchange stays, the doctoral students have the unique opportunity to work at one of Asia's leading universities resp. at a leading European center of innovative mathematical research and to experience the stimulating diversity of scientific cultures.