From Geometry to Quantum Mechanics

Hideki Omori is widely recognized as one of the world’s most creative and original mathematicians. This volume is dedicated to Hideki Omori on the occasion of his retirement from Tokyo University of Science. His retirement was also celebrated in April 2004 with an in?uential conference at the Morito Hall of Tokyo University of Science. Hideki Omori was born in Nishionmiya, Hyogo prefecture, in 1938 and was an undergraduate and graduate student at Tokyo University, where he was awarded his Ph.D degree in 1966 on the study of transformation groups on manifolds [3], which became one of his major research interests. He started his ?rst research position at Tokyo Metropolitan University. In 1980, he moved to Okayama University, and then became a professor of Tokyo University of Science in 1982, where he continues to work today. Hideki Omori was invited to many of the top international research institutions, including the Institute for Advanced Studies at Princeton in 1967, the Mathematics Institute at the University of Warwick in 1970, and Bonn University in 1972. Omori received the Geometry Prize of the Mathematical Society of Japan in 1996 for his outstanding contributions to the theory of in?nite-dimensional Lie groups.

This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori's recent retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas.

The papers focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of partial differential equations and variational methods to geometry. These articles will appeal to graduate students in mathematics and quantum mechanics, as well as researchers, differential geometers, and mathematical physicists.

Contributors include: M. Cahen, D. Elworthy, A. Fujioka, M. Goto, J. Grabowski, S. Gutt, J. Inoguchi, M. Karasev, O. Kobayashi, Y. Maeda, K. Mikami, N. Miyazaki, T. Mizutani, H. Moriyoshi, H. Omori, T. Sasai, D. Sternheimer, A. Weinstein, K. Yamaguchi, T. Yatsui, and A. Yoshioka.