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-0305125Yongbin ruanorbifold是具有最简单奇异性的空间，其中有限群的平滑歧管局部对其进行了局部建模。它们在许多数学和物理学学科中都表现出来。半个世纪的经典理论已经存在。但是它无法捕获Orbifolds的真实本质。在此提案中，主要研究者的原理是系统地研究Orbifolds的“弦乐”几何形状和拓扑，即弦理论中产生的Orbifolds的弦质性质。首席研究员Yongbin Ruan提议系统地研究Orbifolds的弦乐几何形状和拓扑结构。这些很重要的几何对象来自数学的几何和物理学的弦理论，并且涉及数学的许多分支。该提议旨在在这些田野之间建立紧密而富有成果的互动。该项目的概念是跨学科的。物理和数学思想均以必不可少的方式使用。通过研究研讨会，组织和参加国家和国际会议，该提案将增强本科生和研究生的培训，以及阿斯普斯特多拉尔的研究员。