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

研究者和他的同事们研究表征理论、结理论和数学物理之间的相互作用。这些领域相互联系，相互促进。表征理论，在其他方面，帮助数学物理学家预测粒子的存在。它在描述对称性和为共形场论和统计力学提供一种语言方面发挥了重要作用。反过来，数学物理又引导表征理论家们做出了新的猜想、有趣的概括和令人着迷的结果。结和环的不变量，如考夫曼和琼斯的多项式，作为某些代数（Hecke代数，Birman-Wenzl-Murakami代数，辫群的群代数）的表示的迹而出现。当然，通过统计力学等概念，绳结理论与数学物理有关。这次会议促进了研究人员之间的对话，并帮助学生，特别是研究生和最近的博士们熟悉对高性能计算具有重要意义的研究领域。本次研讨会汇集了数学、数学物理和量子计算等许多不同领域的专家。这有助于在可能有助于创建量子计算机的领域进行研究。

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.