Gromov-Witten theory

格罗莫夫-维滕理论

• 批准号: 1103368
• 负责人: Yongbin Ruan
• 金额: $ 30.01万
• 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: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1103368&HistoricalAwards=false
• 关键词: Gromov; Witten; theory

AbstractAward: DMS-1103368Principal Investigator: Yongbin RuanDuring the past twenty years, there has been a great deal ofinteraction between mathematic and physics. Variouscorrespondences or dualities arising from physics have had agreat impact on mathematics. One of these correspondences is theLandau-Ginzburg/Calabi-Yau correspondence. This proposal offers acomprehensive program to establish this correspondence inmathematics with mathematical rigor. There is a wide range ofapplications such as global mirror symmetry, the computation ofGromov-Witten invariants of compact Calabi-Yau manifolds, and tomodular forms.Since the era of Newton, mathematics has been a key tool inhelping us to comprehend the universe. An example isdifferential geometry via Einstein's theory of generalrelativity. During the last twenty years there has been a greatdeal of activity in building so-called string-theoretic models ofthe universe. The string-theoretic model of the universe isten-dimensional, our usual 4-dimensional space-time togeher witha very small 6-dimensional space called a Calabi-Yau manifold.Such a small internal space will affect our space-time throughcertain mathematical quantities such as Gromov-Witteninvariants. The computation of these invariants has been acentral problem in geometry and physics. This is the area inwhich mathematical tools can be very useful. The currentproposal envisages a theoretical framework as well as developingtechnical tools to compute Gromov-Witten invariants

摘要奖：DMS-1103368 首席研究员：阮永斌 在过去的二十年里，数学和物理之间发生了大量的相互作用。 物理学产生的各种对应性或对偶性对数学产生了巨大的影响。这些对应关系之一是兰道-金茨堡/卡拉比-丘对应关系。该提案提供了一个全面的计划，以数学严谨性建立数学上的这种对应关系。 有广泛的应用，例如全局镜像对称、紧致卡拉比-丘流形的格罗莫夫-维滕不变量的计算以及模形式。自牛顿时代以来，数学一直是帮助我们理解宇宙的关键工具。 一个例子是基于爱因斯坦广义相对论的微分几何。在过去的二十年中，在建立所谓的宇宙弦理论模型方面进行了大量的活动。宇宙的弦理论模型是十维的，即我们通常的 4 维时空和一个非常小的称为卡拉比-丘流形的 6 维空间。如此小的内部空间将通过某些数学量（例如格罗莫夫-维滕不变量）影响我们的时空。这些不变量的计算一直是几何和物理学的中心问题。 这是数学工具非常有用的领域。 当前的提案设想了一个理论框架以及开发计算 Gromov-Witten 不变量的技术工具