Braid Groups and Applications
October 16 - 21, 2004
Organizers: Dale Rolfsen (University of BC), Joan Birman (Columbia University), Patrick Dehornoy (University of Caen), Roger Fenn (University of Sussex), Vaughan Jones (UC Berkeley).
Organizers: Dale Rolfsen (University of BC), Joan Birman (Columbia University), Patrick Dehornoy (University of Caen), Roger Fenn (University of Sussex), Vaughan Jones (UC Berkeley).
The basic objective of the workshop is to bring together the world's experts on several different aspects and applications of braid theory. The idea is to share problems and ideas, stimulate new research and hopefully make progress in certain open problems. An example of such a question is whether the Jones representations are faithful and the related question of whether the Jones polynomial characterizes triviality of knots. Algorithmic questions in braid theory will be explored. They have a new importance, due to the possible applications to cryptography. A number of experts in dynamical aspects of braids will be present. We hope to study and extend fascinating connections, for example, between the entropy of a dynamical system described by certain braids and the classical Burau representation. Also present will be experts on the cohomology (and similar properties) of braid groups. As a demonstration of the subtlety of the subject, Fred Cohen has shown that a certain combinatorial question regarding pure braids, if completely answered, would tell us all the homotopy groups of spheres, a notoriously difficult problem in algebraic topology. Another goal of the workshop will be to understand the connections of braid theory with mathematical physics, e. g. quantum field theory, quantum gravity and statistical mechanics.