EXC 2044: Mathematics Münster: Dynamics – Geometry – Structure

我们的集群计划“数学明斯特：动力学-几何学-结构”旨在进一步发展明斯特的数学，使其成为具有高度国际知名度的研究中心。我们将解决根本性的重要数学问题，将数学视为一个有机的整体，有无数的相互作用。我们的研究是统一的三个主要途径：专注于一个给定的问题的底层结构，采取几何的观点和研究相关的动力学群或半群行动。我们将建立的理论不仅将解决正在考虑的问题，而且还将解决许多其他类似性质的问题;这些理论还将提出令人兴奋的新问题。计划集群中的理论数学家在两个合作研究中心内有长期而成功的联合研究记录。最近，应用数学在明斯特一直在强劲发展，与生命科学建立密切的互动。在这一倡议的拟议研究领域之内和之间建立了若干合作关系。计划中的集群将以系统的方式加强现有的互动并激发新的互动。这将导致不同数学领域之间的知识，观点和技术的更大转移。我们计划解决的巨大数学挑战是与数论和表示论相关的Langlands程序的p-adic版本，Baum-Connes和Farrell-Jones的结构作为获得有关流形，数学建模中的结构保持近似和渐近的几何信息的中心工具，为了实现集群的科学和结构目标，我们将遵循三个关键原则：连接数学领域，通过提供广泛的数学培训，建立新的弥合差距教授职位，并加强数学学科之间的国际交流;通过提供有吸引力的硕士、博士和独立的早期职业水平的方案，提供有力的早期职业支持;通过实施有针对性的倡议，平衡家庭和职业，增加妇女在各级学术数学研究中的比例，增加平等机会。

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.