Stringy geometry and topology of orbifold

Orbifold 的弦几何和拓扑

• 批准号: 0305125
• 负责人: Yongbin Ruan
• 金额: $ 43.05万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-06-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0305125&HistoricalAwards=false
• 关键词: Stringy; geometry; topology; orbifold

DMS-0305125Yongbin RuanOrbifold is the space with simplest kind of singularity where it is locally modeled on the quotient of a smooth manifold by a finite group. They appearnaturally in many subjects of mathematics and physics. A classical theory due to Satake has been existed for half of century. But it fails to capture the true nature of orbifolds. In this proposal, the principal investigatorproposes to systematically study "stringy" geometry and topology of orbifolds,i.e., stringy properties of orbifolds arisen from string theory. The principal investigator, Yongbin Ruan, proposes to systematically study what is called the stringy geometry and topology of orbifolds. These areimportant geometric objects arisen from geometry in mathematics and from string theory in physics, and involve with many branches of mathematics. This proposal seeks to develop close and fruitful interactions among thosefields. The project is interdisciplinary in its conception. Both physical and mathematical ideas are used in an essential way. Through research seminar,organizing and participating at national and international conference this proposalwill also enhance the training of undergraduate and graduate students, as well aspostdoctoral fellows.

DMS-0305125用有限群局部模拟光滑流形的商是具有最简单奇异性的空间。它们自然而然地出现在许多数学和物理学科中。萨塔克的经典理论已经存在了半个世纪。但它未能捕捉到奥比诺兹的真实本质。在这一建议中，主要研究者建议系统地研究奥布洛德的“弦”几何和拓扑，即从弦理论中产生的奥布朗德的弦性质。首席研究员阮永斌提出，要系统地研究奥布洛德的弦几何和拓扑学。它们是从数学中的几何和物理中的弦理论中产生的重要几何对象，涉及到数学的许多分支。这项提议寻求在这些领域之间发展密切和富有成效的互动。该项目的概念是跨学科的。物理和数学思想都是以一种基本的方式使用的。通过举办研究研讨会，组织和参加国内和国际会议，该计划还将加强本科生和研究生以及博士后研究员的培养。