Residues and Moduli Spaces of Vector Bundles

向量丛的留数和模空间

基本信息

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

项目摘要

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 该项目涉及代数几何和量子物理学中出现的特殊空间的拓扑不变量：黎曼曲面上抛物线向量丛的模空间。通过将这些模空间的交数与超平面排列理论的某些问题联系起来，可以对它们进行详细的几何分析。将研究拓扑量子场论的新代数几何模型，并探讨与形变量子化的关系。这是代数几何领域的研究。代数几何是现代数学最古老的部分之一，但它在过去四分之一个世纪中得到了革命性的发展，部分原因是最近发现了与量子物理学的一些令人惊讶的联系。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。