International Conference on Special Functions

通过提供航空旅行资金，该团体奖将支持12名美国研究人员参加1999年6月21日至25日在香港城市大学举行的“特殊函数：渐近、调和分析和数学物理”国际研讨会。本次会议旨在为渐近学、经典特殊函数、组合学、调和分析、量子群、数学物理、微分方程和正交多项式等领域的专家提供一个交流思想和了解这些领域最新发展的论坛。最近渐近研究的目标是推导出误差项呈指数级小的展开式。这样的展开式比经典的庞加莱型展开式精确得多，并且有更大的有效区域。特殊函数的谐波分析涉及到根系统、量子矩阵群和经典矩阵群的表示。在过去的几年里，这种方法已经被用来发现关于几个变量的特殊函数（标准函数和q型函数）的新结果。例如，这些方法被用来证明来自代数组合的麦克唐纳猜想，并构造Calogero-Moser-Sutherland型量子多体系统的精确解。特殊函数构成了数学中具有重要基础意义的一大类函数。例如，它们出现在任何具有某种程度对称性的物理现象的建模中，如圆形鼓的振动。会议计划包括邀请一小时的全体演讲，几个平行的半小时演讲，以及对突出问题和未来研究方向的圆桌讨论。预计约有80名与会者。届时将邀请美国、加拿大、荷兰、日本、澳大利亚等国家的研究人员作为演讲嘉宾。本次国际研讨会将促进应用数学家和更多的理论研究人员之间的讨论，以确定可以通过特殊函数解决的应用问题，并将新的数学工具用于应用中。会议将与工业与应用数学学会（SIAM）合作举行，包括SIAM的正交多项式和特殊函数活动小组以及新成立的东南亚分会。

DMS-9815552By 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 MathematicalPhysics, 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, quantumgroups, 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 exponentiallysmall. 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 aboutspecial 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 inthe vibrations of a circular drum. The conference program includes invitedone-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.