Symplectic geometry and group actions

辛几何和群作用

• 批准号: 261958-2008
• 负责人: Karshon, Yael
• 金额: $ 2.11万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503699
• 关键词: Symplectic; geometry; group; actions

Symplectic geometry started out as the geometry underlying Hamilton's equations in classical mechanics. Similar structures appear in Lie theory (the study of continuous symmetries), algebraic geometry (shapes cut out by polynomial equations), quantum (rather than classical) mechanics, and in many more mathematical and physical contexts. Today, symplectic geometry has evolved into a deep mathematical field on its own right. The field is exceptionally broad and interacts with many parts of mathematics and physics; it has gone through rapid developments in the last couple of decades and is an exciting front of international research.

辛几何开始作为几何基础汉密尔顿的方程在经典力学。类似的结构出现在李理论（研究连续对称性）、代数几何（由多项式方程切割出的形状）、量子（而不是经典）力学以及更多的数学和物理背景中。今天，辛几何已经发展成为一个深刻的数学领域的权利。 该领域非常广泛，与数学和物理的许多部分相互作用;它在过去几十年中经历了快速发展，是国际研究的一个令人兴奋的前沿。