Topological solutions

拓扑解决方案

• 批准号: 0905818
• 负责人: Krystyna Kuperberg
• 金额: $ 11.67万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905818&HistoricalAwards=false
• 关键词: Topological; solutions

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The PI investigates the structure of minimal sets in topological dynamical systems and foliations that serve as counterexamples to the Seifert Conjecture and the Modified Seifert Conjecture. The interesting properties of these minimal sets are the topological dimension, the Hausdorff dimension, isolation, and Czech homology in relation to shape theory. Dynamics is also employed in work on problems in discrete and computational geometry.Dynamical systems impact other areas of science. The study of minimal sets is an extension of the study of fixed points and attractors. The theory has application to biology, population research, and economy, in addition to the traditional Science Technology Engineering and Mathematics (STEM) fields. The geometry problems studied by the PI have applications to medical imaging.

该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资助。PI 研究拓扑动力系统和叶状结构中的最小集结构，作为塞弗特猜想和修改塞弗特猜想的反例。这些最小集的有趣属性是拓扑维数、豪斯多夫维数、隔离性以及与形状理论相关的捷克同调性。动力学还用于解决离散几何和计算几何问题。动力学系统影响其他科学领域。极小集的研究是不动点和吸引子研究的延伸。除了传统的科学技术工程和数学（STEM）领域外，该理论还应用于生物学、人口研究和经济。 PI 研究的几何问题可应用于医学成像。