Aspects of Polish group dynamics

波兰团体动态的各个方面

• 批准号: 2246873
• 负责人: Slawomir Solecki
• 金额: $ 36万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2246873&HistoricalAwards=false
• 关键词: Aspects; Polish; group; dynamics

The project will mostly focus on symmetry groups of certain mathematical objects. Two examples of such objects are: a space with a measure and a generic generalized curve. The interest in these objects and their symmetries originates in classical mechanics and in geometric topology, respectively, but they will be investigated using methods coming from a variety of mathematical fields. The interaction of these fields is of independent mathematical interest. The project involves graduate student training.The project will tackle problems on the boundary of Descriptive Set Theory, or more broadly, Logic, Ergodic Theory, and Topology. A precise analysis will be made of closed groups generated by measure preserving transformations. Topological dynamics of the homeomorphism group of a certain canonical continuum, called the pseudoarc, will be investigated. Combinatorial properties related to Ramsey theory of a class of maps of $n$-dimensional simplex will be explored. These diverse themes will be tied together by a point of view coming from Mathematical Logic.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目将主要关注某些数学对象的对称群。此类对象的两个示例是：具有度量的空间和一般的广义曲线。对这些物体及其对称性的兴趣分别源于经典力学和几何拓扑，但将使用来自各个数学领域的方法对它们进行研究。这些场的相互作用具有独立的数学意义。该项目涉及研究生培训。该项目将解决描述集合论，或更广泛地说，逻辑、遍历理论和拓扑的边界问题。将对通过测度保持变换生成的封闭群进行精确分析。将研究某个规范连续统（称为伪弧）的同胚群的拓扑动力学。将探讨与一类 n$ 维单纯形映射的 Ramsey 理论相关的组合属性。这些不同的主题将通过来自数理逻辑的观点联系在一起。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。