Mathematical Sciences: Topology and Geometry of Moduli Spaces of Vectro Bundles

数学科学：Vectro 丛模空间的拓扑和几何

• 批准号: 9504297
• 负责人: Georgios Daskalopoulos
• 金额: $ 3万
• 依托单位: Brown University
• 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: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504297&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Geometry; Moduli

9504297 Daskalopoulos The proposed research lies in the general area of mathematical physics; more specifically, gauge theory. The investigator seeks to gain a better understanding of moduli spaces of vector bundles arising as spaces of solutions to certain problems in theoretical physics and algebraic geometry. Analytic methods such as CR-manifold techniques are to be used to investigate these moduli spaces and their invariants. It is possible that the proposed research will shed light on the relationship between Donaldson and Seiberg-Witten theories. In recent years several unexpected connections between theoretical physics (quantum field theories) and various parts of mathematics (differential topology, and algebraic and differential geometry) have been discovered. Gauge theory began as an attempt to give a unified theoretical framework for describing the four basic forces of nature, and has found many surprising applications in pure mathematics.

小行星9504297 拟议的研究在于数学物理的一般领域;更具体地说，规范理论。调查人员试图获得一个更好的理解模空间的向量丛所产生的空间的解决方案，某些问题的理论物理和代数几何。CR-流形技术等分析方法将用于研究这些模空间及其不变量。这可能有助于我们进一步了解唐纳森理论和塞伯格-威滕理论之间的关系。 近年来，理论物理（量子场论）和数学的各个部分（微分拓扑学、代数几何和微分几何）之间的一些意想不到的联系被发现。规范理论最初试图给出一个统一的理论框架来描述自然界的四种基本力，并在纯数学中发现了许多令人惊讶的应用。