Geometric and group-theoretic studies on differential equations

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We have developed geometric and group-theoretic studies of differential equations, in particular on Monge-Ampere equations, systems of ordinary differential equations, and holonomic systems, in which played a fundamental role the method of nilpotent geometry and analysis developed by N.Tanaka and T.Morimoto.On the occasion of centennial after the death of Sophus Lie, we have organized an International Conference on Lie Groups, Geometric Structures, and Differential Equations -One Hundred Years after Sophus Lie - in Kyoto and Nara from the 13ィイD1thィエD1 to 21ィイD1stィエD1 December, 1999 (Organizers : B.Komrakov, M.Kuranishi, B.Malgrange, T.Morimoto(chairman), H.Sato and K.Yamaguchi).There were given 32 one-hour lectures by 19 mathematicians from abroad and 13 from Japan. More than 120 mathematicians have taken part in this conference. We shall publish the proceedings of the conference first in Kokyuroku(lecture note) of Research Institute for Mathematical Science, Kyoto University and then as a more expanded version in the series of Advanced Studies in Pure Mathematics.Preparatory to this international conference, we have held, in co-operation with International Sophus Lie Center, Japanese-Russian workshop "Towards 100 years after Sophus Lie" in Kazan, Russia from the 7ィイD1thィエD1 to 17ィイD1thィエD1 September, 1998. About 30 participants (11 Japanese) have exchanged their recent research on Lie groups, geometric structures, differential equations and representation theory.As the proceedings to this workshop there have been published in Lobachevskii Journal of Mathematics 3, 4 (1999) twenty-three papers contributed by the participants.