9600274 Curtin This award supports a 12 month Japan Society for the Promotion of Science (JSPS) Postdoctoral Fellowship for Dr. Brian Curtin at the University of Kyushu, Fukuoka, Japan. Dr. Curtin will work with Dr. Eiichi Bannai, professor in the Department of Mathematics, on a research project entitled "Some Problems of Algebraic Combinatorics." The proposed research will examine association schemes using subsonstituent algebra and focusing on connections among the thin condition, the Q-polynomial property, the 2-homogeneous condition, and spin models. The focus of the research will be on spin models, association schemes, and their connections. Spin models arose in the study of knots and links. It has recently been shown that any spin model is contained in an association scheme. In almost every case, the scheme involved satisfies two conditions -- the thin condition and the Q-polynomial condition. Drs. Bannai and Curtin propose to study schemes with both properties from the perspective of the subconstituent algebra, their goal being to determine which of these schemes contain spin models. Spin models have recently received a great deal of attention among researchers at Kyushu University, but until now have not been studied from the perspective of the subconstituent algebra. As association schemes provide the basic framework in the development of codes and designs, research into these basic models will likely result in practical benefits beyond initial theoretical explorations. ***
