Quantum Topology and Hyperbolic Geometry

量子拓扑和双曲几何

• 批准号: 1251399
• 负责人: Stavros Garoufalidis
• 金额: $ 2.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-05-01 至 2014-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1251399&HistoricalAwards=false
• 关键词: Quantum; Topology; Hyperbolic; Geometry

The conference Quantum Topology and Hyperbolic Geometry will be held in Nha Trang, Vietnam, May 13-May 17, 2013. The aim of the conference is to understand how Quantum Field Theory in dimension three detects the topology and geometry of the underlying space. As an example, we will study the connection of the index of a hyperbolic 3-manifold (a remarkable q-series of Dimofte-Gaiotto-Gukov, also studied by Garoufalidis and Garoufalidis-Hodgson-Rubinstein-Segerman) with the asymptotics of the colored Jones polynomial, and with categorification of its integer coefficients. We will also study the recursions of the above q-series and their relation to the AJ and Slope Conjectures, and the relation of the above q-series of Nahm type with thestability of the colored Jones polynomial of alternating links, proven by Garoufalidis-Le.The conference will focus on this new and exciting developments of mathematical physics and their implications to geometry and topology in dimension 3. This is a fertile land of concrete, testable conjectures, symbolic computer experimentation, physics, algebra and low dimensional topology. The opportunities for young researchers are many, and the conference would come in a fortunate timing where the old ideas in quantum topology meet the new ones. The conference website can be found at http://vietnam2013.gatech.edu/.

会议量子拓扑和双曲几何将在芽庄举行，越南，5月13日至5月17日，2013年。会议的目的是了解三维量子场论如何检测底层空间的拓扑和几何。作为一个例子，我们将研究双曲3-流形（Dimofte-Gaiotto-Gukov的一个显著的q-级数，也由Garoufaldine和Garoufalidis-Hodgson-Rubinstein-Segerman研究）的指数与有色琼斯多项式的渐近性以及其整数系数的分类之间的联系。我们还将研究上述q-级数的递归及其与AJ和Slope猜想的关系，以及上述Nahm型q-级数与Garoufalidis-Le证明的交替链接的有色Jones多项式的稳定性的关系。会议将专注于数学物理的这一新的令人兴奋的发展及其对三维几何和拓扑的影响。这是一片肥沃的土地，具体的，可测试的结构，符号计算机实验，物理，代数和低维拓扑。年轻研究人员的机会很多，这次会议将在一个幸运的时机到来，量子拓扑学的旧思想与新思想相遇。会议网站可在http://vietnam2013.gatech.edu/上找到。