A Conference on the Interactions Between Representation Theory, Knot Theory and Mathematical Physics; Potsdam, New York; June 23-28, 2002

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The investigator and his colleagues study interactions between Representation Theory, Knot Theory, and Mathematical Physics. These fields are interrelated and motivate each others' development. Representation theory, among other things, helps mathematical physicists predict the existence of particles. It has played a significant role in describing symmetry and in providing a language for conformal field theory and statistical mechanics. In turn, mathematical physics has led Representation Theorists to new conjectures, interesting generalizations, and fascinating results. Invariants of knots and links such as the polynomials of Kauffman and Jones arise as the trace of representations of certain algebras (Hecke algebras, Birman-Wenzl-Murakami algebras, group algebras of braid groups). And of course, knot theory is related to mathematical physics through concepts such as statistical mechanics. This conference fosters a dialogue between the Researchers, and helps students, in particular graduate students, and recent Ph.Ds become acquainted with the areas of research that is of significant importance to high performance computing. This workshop brings together experts in many different areas of Mathematics, Mathematical physics, and quantum computation, etc. This is helping research in areas that could help creation of quantum computers.