Mathematical Sciences: Intersection Theory Problems from Mathematical Physics

数学科学：数学物理中的交叉理论问题

• 批准号: 9500938
• 负责人: Yue Lin Tong
• 金额: $ 6万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500938&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Intersection; Theory; Problems

9500938 Tong Professor Tong will study problems that derive from the deeper study of intersection theory and moduli spaces. He hopes to study more algebraically the flat projective connections on certain vector bundles over Teichmuller space. He also wishes to study the connections between the BRST differential studied in mathematical physics and the Cech-Koszul complex. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. Algebraic geometry itself is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics. ***

9500938 Tong Tong教授将研究从交叉理论和模空间的更深入研究中衍生的问题。他希望更多地从代数角度研究 Teichmuller 空间上某些向量丛上的平面射影连接。他还希望研究数学物理中研究的 BRST 微分与 Cech-Koszul 复合体之间的联系。 这是代数几何领域的研究，但它直接关系到本世纪理论物理学的两大进步——量子力学和广义相对论。代数几何本身是现代数学最古老的部分之一，但在过去四分之一个世纪里得到了革命性的发展。在它的起源中，它处理可以通过最简单的方程（即多项式）在平面上定义的图形。如今，该领域不仅使用代数方法，还使用分析和拓扑方法，相反，它正在这些领域以及物理学、理论计算机科学和机器人技术中得到应用。 ***