Conference: Number Theory and Combinatorics in Physics; March 21-23, 2003; Gainesville, FL

研究人员与佛罗里达大学共同主办了一场名为“物理学中的数论与组合学”的会议。会议的主要议题是：q超几何函数、Rogers-Ramanujan恒等式、精确可积模型和量子场论；交替符号矩阵和行列式；量子计算；以及Riemann Zeta函数、随机矩阵和量子相关器。这些主题中的每一个都因数学和物理之间的互动而变得更加丰富。例如，当组合数学的交替符号矩阵猜想与统计力学中的XXZ自旋1/2模型(在奇数个位置上)相联系时，人们最近发现了对它的更深层次的理解。在最近的另一个例子中，Di Francesco和他的合作者能够使用共形场理论的方法精确地计算曲折组态指数。会议的主要目标是将数学家和物理学家聚集在一起，讨论和了解这些当前主题的最新发展。这种互动应该有助于促进数学和物理方面的新发展。有11位全体演讲者：乔治·E·安德鲁斯、罗伯特·卡尔德班克、菲利普·迪·弗朗西斯科、丹尼尔·戈特斯曼、金博道夫、巴里·麦科伊、三和哲、詹姆斯·普罗普、迈克尔·鲁宾斯坦、泽维尔·G·维延诺和吴芳云。有13位20分钟的演讲者。多名研究生和新近获得博士学位的S也参加了此次活动。数论研究整数的性质，是数学中最古老的分支之一。在过去的20年里，数论在密码学中有重要的应用。一些现代密码方法的安全性依赖于整数因式分解的复杂性。1994年，彼得·肖尔在理论上展示了如何使用量子计算机大幅降低这种复杂性。量子计算机是基于量子力学原理的，目前只是一种理论装置。量子计算机的概念最初是由诺贝尔奖获得者物理学家理查德·费曼在他著名的加州理工学院计算课程中提出的，时间是1983-1986年。人们相信，未来20年，新一代计算机将是量子计算机。这将需要数学、量子场论和技术的综合。在佛罗里达大学举办的这场名为数论和组合物理学的会议，是一个可以在这样的综合方面取得进展的论坛。

The investigators together with the University of Florida are hosting a Conference, ``Number Theory and Combinatorics in Physics.'' The main topics of the conference are q-hypergeometric functions, Rogers-Ramanujan identities, exactly integrable models and quantum field theory; alternating sign matrices and determinants; quantum computing; and the Riemann zeta-function, random matrices and quantum correlators. Each of these topics has been enriched by interactions between mathematics and physics. For example, deeper understanding of the alternating sign matrix conjecture of combinatorics was recently found when it was connected with the XXZ spin 1/2 model (on an odd number of sites) from statistical mechanics. In another recent example, Di Francesco and collaborators were able to exactly compute meander configuration exponents using methods of conformal field theory. The main goal of the conference is to bring mathematicians and physicists together to discuss and learn recent developments in these current topics. This interaction should help foster new developments in both mathematics and physics. There are eleven plenary speakers: George E. Andrews, Robert Calderbank, Philippe Di Francesco, Daniel Gottesman, Michio Jimbo, Barry McCoy, Tetsuji Miwa, James Propp, Michael Rubinstein, Xavier G. Viennot, and F.Y. Wu. There are thirteen 20 minute speakers. A number of graduate students and recent Ph.D.'s are participating. Number Theory is concerned with properties of integers and is one of the oldest branches of mathematics. In the last 20 years Number Theory has had important applications to cryptography. The security of some modern cryptographic methods depends on the complexity of factoring integers. In 1994, Peter Shor showed theoretically how this complexity could be drastically reduced using a quantum computer. A quantum computer is based on the principles of quantum mechanics and is at present only a theoretical device. The concept of a quantum computer was first introduced by the Nobel prize-winning physicist Richard Feynman in his famous course on computation given at Caltech, 1983-1986. It is believed that in the next 20 years the new generation of computers will be quantum computers. This will necessitate synthesis of mathematics, quantum field theory and technology. This conference, Number Theory and Combinatorics in Physics, hosted at the University of Florida, is a forum where progress on such a synthesis can be made.