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

2005年3月15-20日，将在哥伦比亚大学巴纳德学院举行题为“辫子、链接和测绘班级小组”的会议。辫子群和映射类群的数学长期以来在低维拓扑学和几何学中一直很重要。研究这些群在适当空间上的作用，对几何结构和其他地方的变形和刚性有重要的见解。由Jones开创的这类群的表示理论已成为与算子代数有着密切联系的一个独立领域。由杨-巴克斯特方程的解产生的辫子群表示是量子群理论的基础，并提供了许多与物理的联系。辫子群中的算法问题，如辫子群中的字和共轭问题，是几何群论中的重要例子，并已被应用于公钥密码学。尽管自1975年比尔曼的同名著作出版以来，这些主题已经被广泛研究，但对这些主题的研究一直在加速进行，朝着多个方向，并使用不同的研究和应用方法。会议确定的主要发言者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。会议将提供一个综合会议的单一论坛，将促进不同学科的研究方向和方法的交叉培养。一个重要的目标是为研究生和年轻的研究人员提供对这一广泛研究领域的一致看法。会议的头两天将专门为研究生和研究人员举办介绍性研讨会和工作坊，这些学生和研究人员是该领域的新手。以会议为基础的会议论文集将成为研究人员的持续资源。

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.