EXC 2044: Mathematics Münster: Dynamics – Geometry – Structure

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Our cluster initiative "Mathematics Münster: Dynamics — Geometry — Structure" aims to further develop mathematics in Münster into a research centre with high international visibility.We will tackle fundamentally important mathematical problems, viewing mathematics as an organic whole with countless interactions. Our research is unified by three major approaches: focusing on the underlying structure of a given problem, taking the geometric viewpoint and studying the relevant dynamics of group or semigroup actions. The theories which we will build will not only solve the problems under consideration but also many others of a similar nature; these theories will also raise exciting new questions.The theoretical mathematicians in the planned cluster have a long and successful record of joint research within two Collaborative Research Centres. More recently, applied mathematics in Münster has been developing strongly, building close interactions with the life sciences. Several collaborations have been established within and between the proposed research areas of this initiative. The planned cluster will enhance existing and spark new interactions in a systematic way. This will lead to a much greater transfer of knowledge, viewpoints and techniques between the different mathematical fields.Great mathematical challenges we plan to address are a p-adic version of the Langlands programme relating number theory and representation theory, the conjectures of Baum–Connes and Farrell–Jones as central tools to gain geometric information about manifolds, structure-preserving approximations and asymptotics in mathematical modelling, and geometry-based model reduction in non-linear spaces with important applications in optimisation and computational geometry.In order to reach the scientific and structural goals of the cluster, we will follow three key principles: Connecting Mathematical Fields, by providing broad mathematical training, establishing new Bridging the Gaps professorships and enhancing international exchange across mathematical disciplines; Strong Early Career Support by offering attractive programmes on the master’s, PhD and independent early career levels; and Increasing Equal Opportunity by implementing targeted initiatives to balance family and career and to increase the proportion of women in mathematical research on all academic levels.