XXV International Colloquium on Group Theoretical Methods in Physics

该奖项为参加2004年8月2日至6日在墨西哥科科约克举行的第25届国际物理学集体理论方法研讨会的美国与会者提供旅费和当地费用。这是实践对称方法的物理学家、数学家和工程师社区一年两次的会议。它上一次在北美举行是在1988年，因此它为这一广阔领域的美国初级研究人员提供了一个特别好的机会。会议的目的是回顾近年来取得的主要进展，以连贯一致的形式介绍导致当前这一主题工作的主要成果，以便研究生和新进入该领域的年轻研究人员能够接触到这些成果，并为今后的研究指出最有希望的方向。特别是会议关于“21世纪的群论”的专题小组，旨在为初级研究人员提供指导，会议纪要将出版。群论是关于对称性的数学。现代物理理论广泛使用群论思想来表示自然界中观察到的对称性。元素周期表、原子光谱分析、晶体结构分类和基本粒子理论都涉及群论模型。什么是显式可解的经典或量子力学系统的概念，最好根据系统的对称性来理解。工程领域，如层析成像和信号处理，包括小波、雷达和声纳，都与谐波分析、群函数的扩展和分析密切相关。本次会议探讨了这一重要的多学科领域的最新发展和存在的问题。会议的主要议题是：李群、量子群、表象理论和特殊函数；超对称性、超弦和量子引力；可积性、非线性系统和量子混沌；离散系统和信号分析；量子力学基础；半群、时间不对称和共振；量子计算；线性和非线性光学；核物理、原子和分子物理；基本粒子物理；以及凝聚态和统计物理。

This award furnishes travel and local expenses for U.S. participants in the 25th International Colloquium on Group Theoretical Methods in Physics, held in Cocoyoc, Mexico, 2-6 August 2004. This is the biannual meeting of the community of physicists, mathematicians, and engineers who practice the methods of symmetry. It was last held in North America in 1988, so it provides an especially good opportunity for U.S. junior researchers in this broad field. The purpose of the meeting is to review the principal developments that have occurred in recent years, to present the main results leading to current work in the subject in a coherent form that will be accessible to graduate students and young researchers newly entering the domain, and to point out the most promising directions for future research. In particular, the meeting's special panel on "Group theory in the XXI Century," is meant to provide guidance to junior researchers, and the Proceedings will be published. Group theory is the mathematics of symmetry. Modern physical theories make extensive use of group theoretical ideas to represent the symmetries observed in nature. The periodic table of the elements, atomic spectral analysis, classification of crystal structure, and theories of elementary particles all involve group-theoretic models. The concept of what is an explicitly solvable classical or quantum mechanical system is best understood in terms of the symmetry of the system. Engineering areas such as tomography and signal processing, including wavelets, radar, and sonar, are intimately bound up with harmonic analysis, the expansion and analysis of functions on groups. This conference explores current developments and open problems in this important, multidisciplinary field. The principal topics for the meeting are: Lie groups, quantum groups, representation theory, and special functions; Supersymmetry, superstrings, and quantum gravity; Integrability, nonlinear systems, and quantum chaos; Discrete systems and signal analysis; Foundations of quantum mechanics; Semigroups, time asymmetry, and resonances; Quantum computing; Linear and nonlinear optics; Nuclear, atomic, and molecular physics; Elementary particle physics; and Condensed matter and statistical physics.