Mathematical Sciences: Geometry of Moduli Spaces of Vector Bundles

数学科学：向量丛模空间的几何

• 批准号: 9503635
• 负责人: Richard Wentworth
• 金额: $ 6万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503635&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Moduli; Spaces

9503635 Wentworth This project lies in the area of smooth four-manifolds, more specifically, Donaldson theory. The investigator wants to find necessary and sufficient conditions for the existence of symplectic structures on smooth four-manifolds; to find the Donaldson series for the complex projective plane; to understand how the Donaldson series is affected under certain birational transformations. The modern study of smooth four-dimensional spaces was initiated, in large measure, by the work of Simon Donaldson in the early eighties; Donaldson used ideas from theoretical physics - Yang-Mills equations and gauge theories - in an ingenious way to help classify smooth four-manifolds. It is worth mentioning that Nathan Seiberg and Edward Witten have recently come up with an easier and more direct theory of smooth four-manifolds, again motivated by ideas from theoretical physics, namely monopoles and string theory.

这个项目属于光滑四流形领域，更具体地说，是Donaldson理论。研究光滑四流形上辛结构存在的充分必要条件；求复射影平面的Donaldson级数；以了解唐纳森系列在某些民族转换下是如何受到影响的。光滑四维空间的现代研究在很大程度上是由西蒙·唐纳森（Simon Donaldson）在80年代初的工作发起的；Donaldson巧妙地运用了理论物理学中的思想——Yang-Mills方程和规范理论——来帮助对光滑的四流形进行分类。值得一提的是，Nathan Seiberg和Edward Witten最近提出了一种更简单、更直接的光滑四流形理论，同样受到理论物理学的启发，即单极子和弦理论。