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举办了一场名为“物理学中的数论和组合”的会议。“会议的主要议题是q-超几何函数、罗杰斯-拉马努金恒等式、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;黎曼ζ函数，随机矩阵和量子相关器。数学和物理之间的相互作用丰富了这些主题。例如，最近将组合学的交替符号矩阵猜想与统计力学的XXZ自旋1/2模型（在奇数个位置上）联系起来时，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和他的合作者利用共形场论的方法精确地计算出了弯曲构型指数。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。这种相互作用应该有助于促进数学和物理学的新发展。共有11位全体会议发言人：George E. Andrews、Robert Calderbank、Philippe Di Francesco、Daniel Gottesman、Michio Jimbo、Barry McCoy、Tetsuji Miwa、James Propp、Michael Rubinstein、Xavier G. Viennot和F.Y. Wu。有13个20分钟的演讲者。一些研究生和刚毕业的博士也在参与。数论研究的是整数的性质，是数学最古老的分支之一。在过去的20年里，数论在密码学中有着重要的应用。一些现代密码方法的安全性取决于分解整数的复杂度。1994年，彼得·肖尔（Peter Shor）从理论上展示了如何使用量子计算机大幅降低这种复杂性。量子计算机是以量子力学原理为基础的，目前还只是一种理论设备。量子计算机的概念最早是由诺贝尔奖得主、物理学家理查德·费曼（Richard Feynman）于1983年至1986年在加州理工学院（Caltech）讲授著名的计算课程时提出的。人们相信，在未来20年内，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。这次由佛罗里达大学主办的“物理学中的数论与组合”会议，是一个可以在这种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.