Mathematical Sciences: Symplectic and Complex Geometry

[504898]沃尔夫森提出的研究是在辛几何领域。该研究人员利用非线性偏微分方程和复杂几何的技术来解决辛几何中的某些问题。本文特别讨论了拉格朗日极小曲面和量子上同调群的几个问题。辛几何为经典力学和量子力学中的许多问题提供了一个数学背景。拉格朗日极小曲面是辛几何中的极值对象，它的存在性是一个具有许多可能应用于物理学的基本问题。

9504898 Wolfson The proposed research lies in the area of symplectic geometry. This investigator uses techniques from nonlinear PDEs and complex geometry to tackle certain problems in symplectic geometry. In particular, several problems concerning Lagrangian minimal surfaces and the quantum cohomology group are to be considered. Symplectic geometry provides a mathematical setting for many problems in classical mechanics as well as quantum mechanics. The existence of Lagrangian minimal surfaces, which are extremal objects in symplectic geometry, is a fundamental problem with many possible applications to physics.