Mathematical Sciences: Symplectic Geometry: Moduli Spaces and Manifold Invariants

数学科学：辛几何：模空间和流形不变量

• 批准号: 9403567
• 负责人: Jonathan Weitsman
• 金额: $ 4.91万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403567&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Geometry; Moduli

9403567 Weitsman The research entails the symplectic geometry of moduli spaces associated with Riemann surfaces. The focus will be on the use of methods from the the theory of toric varieties to study moduli spaces of vector bundles and certain conjectures concerning the moduli of curves. It is also planned to study the relation between the symplectic geometry of the moduli space of vector bundles and certain 3-manifold invariants. The research has potential applications to other areas of mathematics and also to quantum gravity and string theory in mathematical physics. ***

9403567魏茨曼研究了与黎曼曲面相关的模空间的辛几何。重点将集中在使用环簇理论的方法来研究向量丛的模空间和关于曲线的模的某些猜想。还计划研究向量丛的模空间的辛几何与某些三维流形不变量之间的关系。这项研究还可能应用于数学的其他领域，以及数学物理中的量子引力和弦理论。***