By providing air travel funds this group award will support twelve U.S. researchers participation in the International Workshop on Special Functions: Asymptotics, Harmonic Analysis, and Mathematical Physics, City University of Hong Kong, June 21-25, 1999. This conference is designed to provide a forum for experts in asymptotics, classical special functions, combinatorics, harmonic analysis, quantum groups, mathematical physics, differential equations, and orthogonal polynomials to exchange ideas and to acquaint participants with the most recent developments in these areas. The goal of recent work in asymptotics is to derive expansions whose error terms are exponentially small. Such expansions give much greater accuracy than the classical Poincare' type expansions and have larger regions of validity. The harmonic analysis aspects of special functions involve root systems and representations of quantum and classical matrix groups. In the last few years, such methods have been used to find new results about special functions (both standard and q-type) of several variables. For example, these methods were used to prove conjectures of Macdonald that came from an algebraic combinatorics setting and to construct exact solutions of quantum many-body systems of Calogero-Moser- Sutherland type.
Special functions form a large family of functions of fundamental importance in Mathematics. For instance, they appear in the modelling of any physical phenomena where there is some degree of symmetry, as in the vibrations of a circular drum. The conference program includes invited one-hour plenary lectures, several parallel sessions of half-hour presentations, and round-table discussions of outstanding problems and future research directions. Approximately eighty participants are expected. Researchers from many countries will be invited as speakers including relatively large delegations from the U.S., Canada, Netherlands, Japan, and Australia. This international workshop will facilitate discussions between applied mathematicians and more theoretical researchers so that applied problems amenable to solutions via special functions can be identified and the new mathematical tools can be utilized in applications. The conference will be held in cooperation with the Society for Industrial and Applied Mathematics (SIAM) including SIAM's Activity Group on Orthogonal Polynomials and Special Functions and the newly chartered South East Asia Section.
