Matheamtical Sciences: Applications of Elliptic PDE's to Gauge Theory, Topology, and Physics

数学科学：椭圆偏微分方程在规范理论、拓扑学和物理学中的应用

• 批准号: 9505170
• 负责人: Edward Miller
• 金额: $ 20.26万
• 依托单位: Polytechnic University of New York
• 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: 1995-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505170&HistoricalAwards=false
• 关键词: Matheamtical; Sciences; Applications; Elliptic; PDE

Miller 9505170 The proposed research deals with various aspects of geometric partial differential equations. Linear elliptic differential operators, gauge field equations, and Yang-Mills-Higgs equations are among the topics to be pursued. Methods from topology, geometry and analysis are to be employed: variational techniques, moduli space techniques, and index theory are to be applied to tackle these partial differential equations. The proposed research may have consequences in smooth manifold theory by uncovering new topological invariants of manifolds. Gauge fields arise naturally in theoretical physics as attempts to unify basic forces of nature. Yang-Mills-Higgs equations have applications in early universe physics and the theory of galactic formation.

米勒9505170 拟议的研究涉及几何偏微分方程的各个方面。线性椭圆微分算子、规范场方程和杨-米尔斯-希格斯方程都是要研究的课题。方法从拓扑学，几何学和分析：变分技术，模空间技术，和指数理论将被应用到解决这些偏微分方程。所提出的研究可能会在光滑流形理论中发现新的拓扑不变量的流形。 规范场在理论物理学中自然出现，试图统一自然界的基本力。杨-米尔斯-希格斯方程在早期宇宙物理学和星系形成理论中有应用。