Developments of nilpotent geometry and nilpotent analysis, and subriemannian geometry

我们发展了幂零几何和幂零分析，并将它们应用于次黎曼几何。特别是，我们发现了一个简单而普遍的原则，它将偏微分方程系统与幂零分析框架中的李代数表示联系起来。我们组织了以下研讨会和专题讨论会：1）几何学在奈良关于四元数结构、CR结构和次黎曼结构，2004年4月12- 14日，奈良华盛顿大学。2）几何学在奈良关于次黎曼几何，2004年12月13- 15日，奈良华盛顿大学。3）RIMS国际研讨会“Cartan几何学的发展和相关数学问题”，2005年10月24- 27日，在RIMS京都大学，从国外邀请的有D.Alekssevsky，R.Bryant，P.Greiner，R.蒙哥马利，P.Nurowski，S.H.Wang，I.Zelenko，M. Zhitomirskii。我们的目标是进一步发展幂零几何和幂零分析，并整合世界各国的相关研究。即将出版的RIMS研讨会记录包含了通过研讨会获得的许多显着成果。

We developed nilpotent geometry and nilpotent analysis and applied them to subriemannian geometry. In particular, we have found a simple and general principle which associates systems of partial differential equations to representations of Lie algebras in the framework of nilpotent analysis.We organized the following workshops and symposium :1)Geometry in Nara on Quaternion structures, CR-structures and subriemannian structures, April 12-14,2004 at Nara WU.2)Geometry in Nara around subriemannian geometries, December 13-15,2004 at Nara WU.3)RIMS International symposium "Developments of Cartan geometry and related mathematical problems", October 24-27,2005, at RIMS Kyoto UnivAmong the invited from abroad were D.Alekssevsky, R.Bryant, P.Greiner, R.Montgomery, P.Nurowski, S.H.Wang, I.Zelenko, M.Zhitomirskii. We aimed to further develop nilpotent geometry and nilpotent analysis and to integrate related researches arising world-wide in various countries. The proceedings of the RIMS Symposium soon to appear contain many remarkable results obtained through the symposium.