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.

宾夕法尼亚大学数学/物理小组研究一系列主题，所有主题都涉及数学和物理思想的重要相互作用。例如* G2 完整度量的几何形状及其在与粒子物理相关的 M 理论紧致化中的作用；* 瞬时子、矢量束和小瞬子跃迁；* 非阿贝尔傅立叶-Mukai 对偶性；* 杂质 M 理论和现实标准模型真空；* 相关的非洲戈布 K 理论五膜和更高边界拓扑场论；* 火热宇宙和相关宇宙学情景的数学；* 与 D 膜相关的三角范畴的稳定性概念；以及* 通过解决奇点的黑洞物理学。小组研究现代几何、超弦物理学和宇宙学丰富的跨学科边界。代数几何中的新思想允许在超弦和 M 理论的背景下制定粒子物理和量子引力的现实理论。 最近，这些想法导致了膜世界、异质M理论和早期宇宙宇宙学的新表述——火热宇宙学的概念。反之，超弦理论中的许多物理概念激发了数学的新研究方向，例如从镜像对称中出现的枚举几何、校准几何的新开花、以及派生范畴、K理论和非洲几何的新结果。 该奖项由代数、数论、通讯学、几何分析和拓扑学项目共同资助。