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.
