Lagrangian Torus Fibration of Calabi-Yau Manifolds and Application to Mirror Symmetry

卡拉比-丘流形的拉格朗日环面纤维及其在镜面对称中的应用

• 批准号: 0104150
• 负责人: Wei-Dong Ruan
• 金额: $ 5.9万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104150&HistoricalAwards=false
• 关键词: Lagrangian; Torus; Fibration; Calabi; Yau

Abstract for DMS - 0104150PI: Wei-Dong RuanDr. Ruan proposes to study the Lagrangian fibration structure of Calabi-Yau manifolds and of more general Kaehler manifolds, and their applications in mirror symmetry and other Kahler geometry problems as well. The objective of the proposed research is to further inderstand the Lagrangian torus fibration structures for moregeneral Calabi-Yau manifolds, exploring the interplay of sympleticgeometry and complex geometry in Kaehler manifolds, as indicated by Kontsevich's categorical mirror symmetry program. Mirror symmetry has its origin in string theory andsays that we have two theories, which appear to be completely distinct, describing the same physics. If we have two different models of the same universe, one can expect that one of the models can fill in the gaps in understanding the other model. This project is towards understanding this symmetry principle.Results from this proposal should be of interest to mathematicians fromvarious disciplines as well as physicists in string theory.

DMS摘要-0104150PI：Wei -Dong Ruandr。 Ruan建议研究Calabi-yau歧管和更一般的Kaehler歧管的拉格朗日纤维化结构，以及它们在镜子对称性和其他Kahler几何问题中的应用。拟议的研究的目的是进一步征服昆虫歧管中的昆虫歧管歧管的Lagrangian圆环纤维化结构，以探索kaehler歧管中的符号测定法和复杂几何形状的相互作用，如Kontsevich的分类镜像对称程序所示。镜面对称性具有其起源于字符串理论，我们有两种理论，它们似乎完全不同，描述了相同的物理学。如果我们有两个不同的宇宙模型，则可以期望其中一个模型可以填补理解另一个模型的空白。这个项目旨在理解这种对称原则。该提案的结果应该引起各种学科的数学家以及弦理论的物理学家的意义。