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

关于表示论、纽结理论和数学物理之间相互作用的会议；

• 批准号: 0202356
• 负责人: Kazem Mahdavi
• 金额: $ 1万
• 依托单位: SUNY College at Potsdam
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-03-15 至 2003-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0202356&HistoricalAwards=false
• 关键词: Conference; Interactions; Between; Representation; Theory

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.

研究者和他的同事们研究表示论，纽结理论和数学物理之间的相互作用。 这些领域相互关联，相互促进。 表示论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语言方面发挥了重要作用。 反过来，数学物理学又导致表示理论家的新成果，有趣的推广，和迷人的结果。 结和链的不变量（例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、辫子群的群代数）的表示的迹而出现。当然，纽结理论通过统计力学等概念与数学物理相关。 本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，和最近的博士熟悉的研究领域，是具有重要意义的高性能计算。该研讨会汇集了数学，数学物理和量子计算等许多不同领域的专家，这有助于研究可能有助于创建量子计算机的领域。