Mathematical Sciences: Differential Geometric Problems Related To Mathematical Physics

数学科学：与数学物理相关的微分几何问题

• 批准号: 8802885
• 负责人: Thomas Parker
• 金额: $ 1.43万
• 依托单位: Brandeis University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1988-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802885&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometric; Problems

Tom Parker will continue his work in gauge theory. This is currently an extremely active and important part of mathematics. It is important in mathematical physics because of its significance in quantum Yang-Mills theory and in topology because of its implications for diffeomorphism types of four dimensional manifolds. The central objects of study are the moduli spaces of self dual connections on vector bundles over a four dimensional Riemannian manifold. Parker's intention is to investigate the geometry of these spaces as Riemannian manifolds. This will build on the present topological descriptions and will help to provide answers to some problems of physical interest.

汤姆帕克将继续他在规范理论方面的工作。这是 目前是数学中非常活跃和重要的一部分。 它在数学物理中很重要，因为它 在量子杨-米尔斯理论和拓扑学中的重要性， 它对四维空间的同构类型的影响 流形 研究的中心对象是self的模空间 四维向量丛上的对偶联络 黎曼流形帕克的意图是调查 几何这些空间作为黎曼流形。这将构建 对目前的拓扑描述，并将有助于提供 一些物理问题的答案。