
The blending of algebra, geometry, and differential equations has a long and distinguished history, dating back to the work of Sophus Lie and Élie Cartan. Overviewing the depth of their influence over the past 100 years presents a formidable challenge. A conference was held on the centennial of Lie's death to reflect upon and celebrate his pursuits, later developments, and what the future may hold. This volume showcases the contents, atmosphere, and results of that conference. Of particular importance are two survey articles: Morimoto develops a synthetic study of Lie groups, geometric structures, and differential equations from a unified viewpoint of nilpotent geometry. Yamaguchi and Yatsui discuss the geometry of higher order differential equations of finite type. Contributed research articles cover a wide range of disciplines, from geometry of differential equations, CRgeometry, and differential geometry to topics in mathematical physics. This volume is intended for graduate students studying differential geometry and analyis and advanced graduate students and researchers interested in an overview of the most recent progress in these fields. Volumes in this series are freely available electronically 5 years postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students studying differential geometry and advanced graduate students and researchers interested in overviewing the most recent progress in these fields. Table of Contents



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