Braids, Links, and Mapping Class Groups; New York, NY; March 15-20, 2005

辫子、链接和映射类组；

• 批准号: 0501702
• 负责人: Walter Neumann
• 金额: $ 2.7万
• 依托单位: Barnard College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-01 至 2006-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0501702&HistoricalAwards=false
• 关键词: Braids; Links; Mapping; Class; Groups

A conference entitled "Braids, links, and mapping class groups"will be held on March 15-20, 2005, at Barnard College/ColumbiaUniversity. The mathematics surrounding braid groups and mappingclass groups has long been important in low dimensional topology andgeometry. Studying actions of these groups on appropriate spaces isyielding essential insights on deformation and rigidity of geometricstructure and elsewhere. The representation theory of these groups,as initiated by Jones, has become a separate field with deepconnections to operator algebras. Braid group representations comingfrom solutions to the Yang-Baxter equation are fundamental to thetheory of quantum groups, and provide many connections with physics.Algorithmic questions, such as the word and conjugacy problems inbraid groups, serve as important examples in geometric group theory,and have been applied to public-key cryptography.Although these subjects have been widely studied since the 1975publication of Birman's book of the same name, research on thesetopics has been proceeding at an accelerating pace, in a multitude ofdirections, and using diverse methods of study and application. Theconference's confirmed main speakers are some of the world's leadingresearchers in the field, including the pioneers of these approaches.The conference will provide a single forum for a comprehensivemeeting, which will promote cross-fertilization of research directionsand methods across diverse disciplines. An important goal is toprovide graduate students and young researchers with a coherent viewof this wide-ranging research area. The first two days of theconference will be dedicated to introductory seminars and workshopsfor graduate students and researchers who are new to this area. A proceedings volume based on the conference will be a continuing resource for researchers.

题为“辫子、链接和映射班级组”的会议将于 2005 年 3 月 15 日至 20 日在巴纳德学院/哥伦比亚大学举行。 长期以来，围绕辫子群和映射类群的数学在低维拓扑和几何中一直很重要。研究这些群体在适当空间上的行为，可以对几何结构和其他地方的变形和刚性产生重要的见解。 The representation theory of these groups,as initiated by Jones, has become a separate field with deepconnections to operator algebras. 来自 Yang-Baxter 方程解的辫子群表示是量子群理论的基础，并提供了与物理学的许多联系。算法问题，例如辫子群中的词和共轭问题，是几何群论中的重要例子，并已应用于公钥密码学。尽管自 1975 年 Birman 出版同一本书以来，这些主题已得到广泛研究 顾名思义，这些主题的研究一直在加速、朝多个方向、并使用不同的研究和应用方法进行。 会议确定的主要发言人是该领域的一些世界领先的研究人员，包括这些方法的先驱。会议将为综合会议提供一个单一的论坛，这将促进不同学科的研究方向和方法的交叉融合。 一个重要的目标是为研究生和年轻研究人员提供对这一广泛研究领域的连贯观点。 会议的前两天将专门为刚接触该领域的研究生和研究人员举办介绍性研讨会和讲习班。基于该会议的会议记录卷将成为研究人员的持续资源。