Developments of nilpotent geometry and nilpotent analysis, and subriemannian geometry

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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.