Stringy geometry and topology of orbifold

DMS-0305125阮永斌Orbifold是一个具有最简单奇异性的空间，它被一个有限群局部地模拟在一个光滑流形的商上。它们自然地出现在数学和物理的许多学科中。一个由佐竹提出的经典理论已经存在了半个世纪。但它没有捕捉到眶褶的真正本质。在这一建议中，主要作者建议系统地研究轨道褶皱的“弦”几何和拓扑，即，从弦理论中产生的轨道折叠的弦性质。首席研究员阮永斌（Yongbin Ruan）建议系统地研究所谓的轨道褶皱的弦几何和拓扑。它们是数学中源于几何学、物理学中源于弦论的重要几何对象，涉及数学的许多分支。这项建议旨在发展这些领域之间密切和富有成效的互动。该项目在概念上是跨学科的。物理和数学思想都以一种基本的方式被使用。通过研究研讨会，组织和参加国家和国际会议，这一提议还将加强对本科生和研究生以及博士后研究员的培训。

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.