Mathematical Sciences: Study of Association Schemes and Their Character Tables

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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.