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.

宾夕法尼亚州数学/物理小组研究了一系列主题，所有涉及数学和物理学的思想相互作用。 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现代几何形状的边界，超弦物理学和宇宙学。新思想的几何形状使粒子物理学的现实理论和量子重力在s词和理论的背景下提出。 最近，这些想法导致了brane世界的概念，异性M理论以及早期宇宙宇宙学的新表述，即ekpyrotic宇宙学。在反向方向流动，超声理论中的许多物理概念动机研究了数学的研究方向，例如来自镜像对称性的枚举几何形成，校准的几何形状的新开花以及派生类别的新成果，K-They和Gerbes。 该奖项由代数理论和联合学，几何分析和拓扑的计划中的计划进行了奖励。