EXC 2044: Mathematics Münster: Dynamics – Geometry – Structure

我们的群组计划“数学明斯特：动力学-几何-结构”旨在将明斯特的数学进一步发展成为具有高度国际知名度的研究中心。我们将从根本上解决重要的数学问题，将数学视为一个具有无数互动的有机整体。我们的研究被三种主要方法统一起来：关注给定问题的潜在结构，采取几何观点，研究群或半群行动的相关动力学。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。计划中的集群中的理论数学家在两个合作研究中心内进行联合研究的长期和成功的记录。最近，应用数学在明斯特得到了强劲的发展，与生命科学建立了密切的互动。在这一倡议的拟议研究领域内和之间建立了若干合作。计划中的集群将以系统的方式加强现有的并引发新的互动。这将导致不同数学领域之间知识、观点和技术的更大程度的转移。我们计划解决的重大数学挑战是与数论和表示论有关的朗兰兹计划的p-ady版本，作为获得关于流形的几何信息的中心工具的Baum-Connes和Farrell-Jones猜想，数学建模中的结构保持近似和渐近性，以及在优化和计算几何中的重要应用的基于几何的非线性空间的模型简化。为了达到集群的科学和结构目标，我们将遵循三个关键原则：连接数学场，通过提供广泛的数学培训，建立新的教授职位，加强数学学科间的国际交流；通过提供有吸引力的硕士、博士和独立早期职业课程，为早期职业提供强有力的支持；通过实施有针对性的举措，平衡家庭和职业，增加妇女在所有学术水平的数学研究中的比例，从而增加平等机会。

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.