A conference entitled "Braids, links, and mapping class groups" will be held on March 15-20, 2005, at Barnard College/Columbia University. The mathematics surrounding braid groups and mapping class groups has long been important in low dimensional topology and geometry. Studying actions of these groups on appropriate spaces is yielding essential insights on deformation and rigidity of geometric structure and elsewhere. The representation theory of these groups, as initiated by Jones, has become a separate field with deep connections to operator algebras. Braid group representations coming from solutions to the Yang-Baxter equation are fundamental to the theory of quantum groups, and provide many connections with physics. Algorithmic questions, such as the word and conjugacy problems in braid 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 1975 publication of Birman's book of the same name, research on these topics has been proceeding at an accelerating pace, in a multitude of directions, and using diverse methods of study and application. The conference's confirmed main speakers are some of the world's leading researchers in the field, including the pioneers of these approaches. The conference will provide a single forum for a comprehensive meeting, which will promote cross-fertilization of research directions and methods across diverse disciplines. An important goal is to provide graduate students and young researchers with a coherent view of this wide-ranging research area. The first two days of the conference will be dedicated to introductory seminars and workshops for graduate students and researchers who are new to this area. A proceedings volume based on the conference will be a continuing resource for researchers.
