International Conference on Special Functions

DMS-9815552该团体奖将资助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。本次会议的目的是提供一个论坛的专家在渐近，经典的特殊功能，组合学，谐波分析，量子群，数学物理，微分方程，正交多项式交流思想和熟悉的参与者在这些领域的最新发展。最近渐近工作的目标是导出误差项指数小的展开式。这种展开式比经典的庞加莱型展开式具有更高的精度和更大的有效区域。特殊函数的调和分析方面涉及量子和经典矩阵群的根系和表示。在过去的几年里，这种方法已被用来寻找多元特殊函数（包括标准函数和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学设置的麦克唐纳定理，并构造Calogero-Moser-Sutherland型量子多体系统的精确解。特殊函数是数学中一个重要的函数家族。例如，它们出现在任何具有某种程度对称性的物理现象的模型中，如圆形鼓的振动。会议计划包括邀请一个小时的全体演讲，几个半小时的平行会议，以及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。来自许多国家的研究人员将被邀请作为演讲者，包括来自美国，加拿大、荷兰、日本和澳大利亚。 这个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，以便通过特殊函数可以确定适合解决的应用问题，并在应用中使用新的数学工具。会议将与工业和应用数学学会（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.