Residues and Moduli Spaces of Vector Bundles

向量丛的留数和模空间

• 批准号: 9870053
• 负责人: Andras Szenes
• 金额: $ 9.92万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870053&HistoricalAwards=false
• 关键词: Residues; Moduli; Spaces; Vector; Bundles

Szenes 9870053 The project is concerned with topological invariants of special spaces arising both in algebraic geometry and quantum physics: the moduli spaces of parabolic vector bundles over Riemann surfaces. A detailed geometric analysis of the intersection numbers of these moduli spaces will be pursued by relating them to certain problems of the theory of hyperplane arrangements. A new algebro-geometric model of topological quantum field theories will be studied and relations with deformation quantization will be explored. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century, partly due to some recently discovered surprizing connections with quantum physics. 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.

Szenes 9870053该项目与代数几何形状和量子物理学出现的特殊空间的拓扑不变性有关：抛物线矢量束的模量空间在Riemann表面上。 通过将它们与超平面布置理论的某些问题联系起来，可以追求对这些模量空间的交叉数的详细几何分析。将研究一个新的拓扑量子场理论的代数几何模型，并将探讨与变形量化的关系。 这是代数几何学领域的研究。 代数几何形状是现代数学最古老的部分之一，但在过去的25年中，它具有革命性的开花，部分原因是最近发现了一些与量子物理学的惊喜联系。它起源于它处理的数字可以通过最简单的方程（即多项式）在平面中定义的数字。如今，该领域不仅利用了来自代数的方法，还利用了分析和拓扑的方法，相反，在这些领域以及物理，理论计算机科学和机器人技术中找到了应用。