Gromov-Witten Theory and its Applications

格罗莫夫-维滕理论及其应用

• 批准号: 0803193
• 负责人: Yongbin Ruan
• 金额: $ 30.32万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0803193&HistoricalAwards=false
• 关键词: Gromov; Witten; Theory; its; Applications

AbstractAward: DMS-0803193Principal Investigator: Yongbin RuanDuring the past twenty years, there has been a great deal ofinteraction between mathematics and physics. An important area ofthis interaction involves the theory of Gromov-Witteninvariants. In physics, it counts the instantons corrections ofCalabi-Yau space. In mathematics, it provides importantinvariants for algebraic and symplectic geometry. Inspired byboth mathematics and physics, Gromov-Witten theory has beenestablished in a variety of situations such as relativeGromov-Witten theory and orbifold Gromov-Witten theory. Each ofthem is an integral part of the big picture and they have beenessential for a complete understanding of Gromov-Wittentheory. This proposal seeks to advance Gromov-Witten theory intwo directions; (i) expanding Gromov-Witten theory to theLandau-Ginzburg/singularities model and developing it as aneffective computational tool for ordinary Gromov-Witten theory;(ii) applying Gromov-Witten theory to study symplectic birationalgeometry.Mathematics is always an important tool and language in ourunderstanding of the structure of the universe we live in. Inthe string theoretic model of the universe, modern mathematicalsubjects such as geometry and topology play an ever biggerrole. In particular, Gromov-Witten invariants enter these modelsas important physical quantities called instantoncorrections. This project will improve our ability to calculateinstanton corrections and hence enhance our understanding of thepossible structure of the universe.

AbstractAward：DMS-0803193主要研究者：阮永斌在过去的二十年里，数学和物理之间有着大量的相互作用。这种相互作用的一个重要领域涉及Gromov-Witteninvariants理论。在物理学中，它计算Calabi-Yau空间的瞬子修正。在数学上，它为代数几何和辛几何提供了重要的不变量。Gromov-Witten理论受到数学和物理学的启发，在各种情况下都得到了建立，如相对Gromov-Witten理论和轨道Gromov-Witten理论。他们每个人都是一个整体的一部分，他们一直是必不可少的一个完整的理解格罗莫夫-维滕理论。这一提议试图在两个方向上推进Gromov-Witten理论：（i）将Gromov-Witten理论扩展到Landau-Ginzburg/奇点模型，并将其发展为普通Gromov-Witten理论的有效计算工具;（ii）将Gromov-Witten理论应用于辛双有理几何的研究。 在弦理论的宇宙模型中，几何学和拓扑学等现代物理学科扮演着越来越重要的角色。特别是，Gromov-Witten不变量进入这些模型作为重要的物理量称为instantoncorrection。该项目将提高我们计算瞬子修正的能力，从而增强我们对宇宙可能结构的理解。