FRG: The Geometry of Superstrings

FRG：超弦几何

• 批准号: 0139799
• 负责人: Ron Donagi
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2008-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0139799&HistoricalAwards=false
• 关键词: FRG; Geometry; Superstrings

The Penn Math/Physics group studies a range of topics, all involvingsignificant interactions of ideas from mathematics and physics.For example* the geometry of metrics with G2 holonomy and their role in M-theorycompactifications which are relevant to particle physics;* instantons, vector bundles, and small instanton transitions;* non-Abelian Fourier-Mukai duality;* heterotic M-theory and realistic standard model vacua;* K-theory of gerbes as it relates to both fivebranes and higher boundarytopological field theories;* the mathematics of the Ekpyrotic universe and related cosmologicalscenarios;* notions of stability in triangulated categories as they relate toD-branes;and* black-hole physics via resolution of singularities.The Penn Math/Physics group studies the rich interdisciplinary boundariesof modern geometry, superstring physics and cosmology. New ideas inalgebraic geometry have allowed the formulation of realistic theories ofparticle physics and quantum gravitation within the context ofsuperstrings and M-theory. Recently, these ideas have led to the conceptsof brane worlds, heterotic M-theory and a new formulation of the cosmologyof the early universe, Ekpyrotic cosmology. Flowing in the reversedirection, many of the physical concepts in superstring theory motivatenew research directions in mathematics, such as the enumerative geometryemerging from mirror symmetry, the new flowering of calibrated geometries,and new results in derived categories, K-theory and gerbes. This award is cofunded by the Programs in Algebra, Number Theory, and Cominatorics, Geometric Analysis, and Topology.

宾大数学/物理小组研究一系列的主题，所有的都涉及到数学和物理思想的重要相互作用。例如 * 度量的几何与G2完整性及其在M-理论紧化中的作用，这与粒子物理学有关;* 瞬子，矢量束和小瞬子跃迁;* 非阿贝尔傅立叶-向井对偶;* 杂种M-理论和现实标准模型真空;* 非对称M-理论和现实标准模型真空。* K理论的gerbes，因为它涉及到五膜和更高的边界拓扑场论;* 数学的Ekpyrotic宇宙和相关的cosmologicalscenarios;* 概念的稳定性在三角范畴，因为它们涉及到D膜;和 * 黑洞物理学通过解决奇点。宾夕法尼亚大学数学/物理组研究现代几何学的丰富的跨学科边界，超弦物理学和宇宙学代数几何中的新思想使得在超弦和M理论的背景下，粒子物理学和量子引力的现实理论得以形成。 最近，这些想法导致了膜世界的概念，杂化M理论和早期宇宙的新宇宙学，Ekpyrotic宇宙学。超弦理论中的许多物理概念以相反的方向流动，激发了数学中新的研究方向，例如从镜像对称中出现的枚举几何，校准几何的新开花，以及派生类别，K理论和gerbes的新结果。 该奖项由代数，数论和Cominatorics，几何分析和拓扑学计划共同资助。