FRG: The Geometry of Superstrings

宾夕法尼亚大学数学/物理小组研究一系列主题，所有这些主题都涉及数学和物理思想的重要相互作用。例如，具有G2完整度规的几何及其在与粒子物理相关的m理论紧化中的作用；*瞬子，矢量束，和小瞬子转换；*非阿贝尔Fourier-Mukai对偶；*异质性m理论与现实标准模型真空；* gerbes的k -理论，因为它涉及到五膜和更高的边界拓扑场论；*热释宇宙的数学和相关的宇宙学情景；*与d膜相关的三角化范畴的稳定性概念；以及通过奇点解析的黑洞物理学。宾夕法尼亚大学数学/物理小组研究现代几何、超弦物理和宇宙学等丰富的跨学科边界。在超弦和m理论的背景下，代数几何中的新思想使得粒子物理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，异质m理论和早期宇宙宇宙学的新公式，Ekpyrotic宇宙学。相反，超弦理论中的许多物理概念激发了数学中新的研究方向，例如从镜像对称中出现的计数几何，校准几何的新发展，以及衍生类别，k理论和gerbes的新结果。该奖项由代数、数论、数论、几何分析和拓扑学项目共同资助。

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.