| Co-Investigator(Kenkyū-buntansha) |
MUNEMASA Akihiro Tohoku University, Graduate School of Information Science, Professor, 大学院・情報科学研究科, 教授 (50219862)
BANNAI Etsuko KYUSHU UNIVERSITY, Faculty of Mathmatics, Associate Professor, 大学院・数理学研究院, 助教授 (00253394)
ITO Tatsuro Komazawa University, Faculty of Science, Professor, 理学部, 教授 (90015909)
SUZUKI Hiroshi International Christian University, College of Liberal Arts, Professor, 教養学部, 教授 (10135767)
KOIKE Masao KYUSHU UNIVERSITY, Faculty of Mathmatics, Professor, 大学院・数理学研究院, 教授 (20022733)
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| Research Abstract |
One of the goal of this grant is to widely contribute to the advancement of algebraic combinatorics in Japan through workshops and travel aid. During the fiscal year 2001-2003, the grant was used to partly support : The 18th, 19th, 20th Algebraic Combinatoric Symposiums (at resp. Chiba University, Kumamoto University, Hokkaio University), three symposiums entitled "Algebraic Combinatorics" at RIMS, three workshops on areas related to automorphic forms at Hamamatsu (Ibukiyama, Bannai, Saito, Miyamoyo organizers). Symposium at Yamagata (Nov. 2002), International Conference EA- CAC2 held in Fukuoka (Bannai organizer, Nov. 2003).
Research in Algebraic Combinatorics in Japan is showing steady progress. The progress covers diverse areas such as distant-regular graphs, association schemes, codes, designs, lattices, modular forms. The results of the principal invstigator includes: (i) Character tables of commutative association schemes and Ramanujan graphs, (ii) Relations between codes, lattices and modular forms, (iii) Tight 4-, 5-, 7-designs on spheres (Bannai Munemasa-Venkov), (iv) Tight designs/codes over Grassmanian spaces (Bachoo-Bannal Coulangeon). In addition, the pricinpal investigator studied designs on Euclidean spaces: Collaborating with Etsuko Bannai, the classification of tight 4-designs with constant weight, the classification of Gaussian tight 4-designs, and the classification of optimal tight 4-designs on two concentric spheres were completed. We are currently challenging more general classi-fications. Jointly with Makoto Tanabe, we participated in the verification of Oleg Musin's spectacular result: The determination of the Kissing number in dimension four, and helped the completion of Musin's proof.
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