Mathematical Sciences: Symplectic Topology & Riemannian Geometry of Lagrangian Submanifolds

9504455哦 拟议的研究在于辛拓扑和几何的一般领域。更具体地说，研究者建议研究Floer上同调和拉格朗日子流形。预计这样的研究将导致拉格朗日嵌入和浸入问题的新技术。此外，研究人员建议考虑特殊拉格朗日子流形的曲率估计问题-这可能会在极小子流形理论中产生分歧。 辛几何为经典力学和量子力学中的许多问题提供了严格的数学背景。拉格朗日子流形是辛几何中的基本对象-它们在某种意义上是极值对象-Floer上同调是研究它们的强大拓扑工具。

9504455 Oh The proposed research lies in the general area of symplectic topology and geometry. More specifically, the investigator proposes to study Floer cohomology and Lagrangian submanifolds. It is expected that such a study will lead to new techniques for Lagrangian embedding and immersion problems. In addition, the investigator proposes to consider curvature estimate problems for special Lagrangian submanifolds - this may have ramifications in minimal submanifold theory. Symplectic geometry provides a rigorous mathematical setting for many problems in classical and quantum mechanics. Lagrangian submanifolds are fundamental objects - they are extremal objects in some sense - in symplectic geometry, Floer cohomology is a powerful topological tool for their study.