Mathematical Sciences: Study of Association Schemes and Their Character Tables

该奖项支持俄亥俄州立大学班奈荣一教授在代数组合学方面的研究。他将研究P-多项式和q -多项式关联方案，距离正则图和有向图，以及大类数的一般交换关联方案。他的研究强调了代数组合学与有限群理论、正交多项式理论和各种表示理论（包括经典群和Chevalley群的表示理论）的相互作用。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学代表了对所有数学活动——计数——的系统化。然而，在其现代发展中，组合学已经不仅仅是计算，而是利用了各种各样的先进数学技术，尽管它的根源可以追溯到几个世纪以前，但由于它在通信和信息技术中的重要性，该领域在过去的几十年里有了爆炸性的发展。

This award supports the research in Algebraic Combinatorics of Professor Eiichi Bannai of Ohio State University. He will study P- and Q-polynomial association schemes, distance-regular graphs and digraphs, and general commutative association schemes of large class number. His research emphasizes the interplay of algebraic combinatorics with the theory of finite groups, with the theory of orthogonal polynomials, and with various representation theories, including the representation theory of classical and Chevalley groups. This research falls in the broad category of Combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, Combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, Combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.