Collaborative Research: The Geometry of Duality in Mathematics and Physics

合作研究：数学和物理中的对偶几何

• 批准号: 0074329
• 负责人: Cumrun Vafa
• 金额: $ 66万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074329&HistoricalAwards=false
• 关键词: Collaborative; Research; Geometry; Duality; Mathematics

AbstractAward: DMS-0074329Principal Investigator: Cumrun VafaThis research project assembles a team at two campuses to work onstring theory and related geometry. The project is led by twomathematicians and a physicist, and the award supportspostdoctoral research fellows, graduate students, and thecollaborations and communications of a broadly based researchnetwork. The research program supported by this awardconcentrates on dualities in string theory and M theory, a topicin which a broad range of geometric and physical concepts cometogether. The best known of these dualities is mirror symmetry,which has had dramatic consequences for algebraic and symplecticgeometry, and this project intends to explore new dualities andconstraints along with mirror symmetry.String theory is a promising candidate for a unifying theory ofthe universe at its most fundamental levels. The basic idea issimple - elementary particles should be modeled as mathematicalloops of string rather than as points - but working out thedetails of this theory has involved and inspired somesophisticated mathematical tools and ideas. Constraints andobservations from physics, sometimes posed as a claim that twodistinct geometries must generate the same physical theory, canhave large numbers of consequences for geometry since quantitiesof physical interest are often expressed as the average value ofan observable quantity over space, or as a way of counting thenumber of times two objects meet.

AbstractAward：DMS-0074329首席研究员：Cumrun Vafa这个研究项目在两个校区组建了一个团队，研究弦理论和相关的几何学。 该项目由两名数学家和一名物理学家领导，该奖项支持博士研究员、研究生以及基础广泛的研究网络的合作和交流。 该奖项支持的研究项目集中在弦理论和M理论的对偶性上，这是一个广泛的几何和物理概念结合在一起的主题。 这些对偶性中最著名的是镜像对称，它对代数和辛几何产生了巨大的影响，本项目打算探索新的对偶性和镜像对称的约束沿着。弦理论是在最基本层次上统一宇宙理论的一个有希望的候选者。 基本思想很简单--基本粒子应该被模拟成弦的椭圆环而不是点--但是要想弄清楚这个理论的细节，就需要用到复杂的数学工具和思想，并激发了它们的灵感。 来自物理学的约束和观察，有时候被认为是两种不同的几何必须产生相同的物理理论，可以对几何学产生大量的影响，因为物理感兴趣的量通常被表示为空间上可观察量的平均值，或者作为计算两个物体相遇次数的一种方法。