Mathematical Sciences: Symplectic Geometry and Euclidean Geometry

数学科学：辛几何和欧几里得几何

• 批准号: 9504134
• 负责人: John Millson
• 金额: $ 9万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504134&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Geometry; Euclidean

9504134 Millson The proposed research lies in the interface of topology and geometry. Working on the classical problem of classifying linkages in space, the investigator has found connections to representation theory and algebraic geometry. To be more specific, the proposed research seeks to develop parallels between the singularities in the representation varieties of Coxeter groups and the singularities in the deformation spaces of linkages. A linkage in space can model a robot arm and other rigid structures with joints; a topological classification of possible linkages in space may turn out to have ramifications in control theory and robotics.

9504134 Millson 提议的研究在于拓扑和几何的接口。通过研究空间中联系分类的经典问题，研究人员发现了与表示论和代数几何的联系。更具体地说，所提出的研究旨在开发 Coxeter 群表示多样性中的奇点与链接变形空间中的奇点之间的相似性。 空间连杆可以模拟机器人手臂和其他带有关节的刚性结构；对空间中可能的联系进行拓扑分类可能会对控制理论和机器人技术产生影响。