FRG: The Geometry of Superstrings

宾夕法尼亚大学数学/物理小组研究了一系列主题，所有这些主题都涉及到来自数学和物理的重要思想的相互作用。例如，*具有G2完整理论的度规的几何及其在与粒子物理相关的M理论紧凑化中的作用；*瞬子、矢量丛和小瞬子跃迁；*非阿贝尔傅立叶-穆凯对偶性；*异质M理论和现实的标准真空模型a；*细菌的K理论，因为它与五层膜和更高边界的拓扑场理论有关；*热解宇宙的数学和相关的宇宙学场景；*三角范畴中的稳定性概念，因为它们与TOD-BRAN有关；宾夕法尼亚大学数学/物理学小组研究现代几何学、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理论的背景下提出现实的粒子物理和量子引力理论。最近，这些想法导致了膜世界的概念，杂化的M理论，以及早期宇宙的宇宙学的新公式，热学宇宙学。相反，超弦理论中的许多物理概念推动了数学中新的研究方向，如从镜像对称中出现的计数几何，校准几何的新开花，以及派生范畴、K理论和GERBES的新结果。该奖项由代数、数论、数学、几何分析和拓扑学等课程共同资助。

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.