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

2005年3月15日至20日，在巴纳德学院/哥伦比亚大学将举行一次题为“辫子、链接和绘图班级“的会议。 围绕辫子群和映射类群的数学在低维拓扑学和几何学中一直很重要。研究这些群体在适当空间上的作用，对几何结构的变形和刚性等方面有重要的意义。 这些群的表示论，由琼斯发起，已经成为一个独立的领域，与算子代数有着深刻的联系。 由杨-巴克斯特方程的解得到的辫群表示是量子群论的基础，并提供了与物理学的许多联系。数学问题，如辫群中的字和共轭问题，是几何群论中的重要例子，并已应用于公共领域-尽管自1975年Birman的同名书籍出版以来，这些主题已被广泛研究，但对这些主题的研究一直在加速进行，在多个方向，并使用不同的研究和应用方法。 会议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。会议将提供一个综合性会议的单一论坛，这将促进跨学科研究方向和方法的交叉施肥。 一个重要的目标是为研究生和年轻的研究人员提供一个连贯的观点，这一广泛的研究领域。 会议的前两天将致力于介绍研讨会和研讨会的研究生和研究人员谁是新的这一领域。一个会议记录卷的基础上，将是一个持续的资源，为研究人员。

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.