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Geometric and group-theoretic studies on differential equations

微分方程的几何和群论研究

基本信息

批准号：
10440019
负责人：
MORIMOTO Tohru
金额：
$ 2.94万
依托单位：
Nara Women's University (1999)Kyoto University of Education (1998)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

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.

我们发展了微分方程的几何和群论研究，特别是Monge-Ampere方程，常微分方程组和完整系统，其中N.Tanaka和T.Morimoto发展的幂零几何和分析方法发挥了基础作用。在Sophus Lie去世一百周年之际，我们组织了李群，几何结构，和微分方程-Sophus Lie之后一百年-1999年12月13日至21日在京都和奈良举行（组织者：B.Komrakov、M.Kuranishi、B.Malgrange、T.Morimoto（主席）、H.Sato和K.Yamaguchi）。来自国外的19位数学家和来自日本的13位数学家进行了32场一小时的讲座。超过120名数学家参加了这次会议。我们将首先在Kokyuroku出版会议记录（讲座笔记）的研究所数学科学，京都大学，然后作为一个更扩大的版本在一系列的高等研究纯数学。筹备这次国际会议，我们举行了，在合作与国际索菲斯李中心，日俄研讨会“走向100年后索菲斯李”在喀山，俄罗斯从1998年9月7日至17日。大约30名与会者（11名日本人）交流了他们最近在李群，几何结构，微分方程和表示论方面的研究。作为这次研讨会的会议记录，在Lobachevskii Journal of Mathematics 3，4（1999）上发表了与会者贡献的23篇论文。