The theories which we 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 research areas of this initiative.

The cluster enhances existing and sparks 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 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 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.