Mathematical Sciences: Symplectic and Complex Geometry

数学科学：辛几何和复几何

• 批准号: 9504898
• 负责人: Jon Wolfson
• 金额: $ 7.5万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504898&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Complex; Geometry

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.

9504898沃尔夫森建议的研究领域是辛几何。这位研究者利用非线性偏微分方程组和复几何中的技巧来解决辛几何中的某些问题。特别地，要考虑有关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，它的存在是一个基本问题，在物理学中有许多可能的应用。