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

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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.