"Symplectic topology, generalized geometry and applications"

我的研究方向是微分几何，这是纯数学的一个领域，研究某些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。在数学上，这些属性是这些形状上的额外结构或对称性，或不同类型形状之间的关系。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，我的计划涉及辛流形，拉格朗日子流形，和广义几何希钦发起。

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.