"Symplectic topology, generalized geometry and applications"

《辛拓扑、广义几何及其应用》

• 批准号: 418535-2012
• 负责人: Hu, Shengda
• 金额: $ 1.46万
• 依托单位: Wilfrid Laurier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=551471
• 关键词: Symplectic; topology; generalized; geometry; applications

My research program lies in the field of differential geometry, an area of pure mathematics, which studies certain kinds of geometrical shapes and configurations of these shapes. It is intimately related to the physical world, since the descriptions of physical systems, both classical and quantum systems, often require geometrical shapes with certain special properties. Mathematically, such properties are extra structures on or symmetries of these shapes, or relations among shapes of different types. The mathematical study of these properties would help the understanding of the corresponding physical systems. More specifically, my program concerns symplectic manifolds, Lagrangian submanifolds, and generalized geometry initiated by Hitchin.

我的研究项目是微分几何领域，这是一个纯数学领域，研究某些类型的几何形状和这些形状的配置。它与物理世界密切相关，因为对物理系统的描述，无论是经典系统还是量子系统，通常都需要具有某些特殊性质的几何形状。从数学上讲，这种性质是这些形状上的额外结构或对称性，或者不同类型的形状之间的关系。对这些性质的数学研究将有助于理解相应的物理系统。更具体地说，我的程序涉及辛流形、拉格朗日子流形和希钦开创的广义几何。