From Geometry to Quantum Mechanics: In Honor of Hideki Omori (Progress in Mathematics Book 252)

* Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference Curriculum Vitae / Hideki Omori -- Pt. I. Global Analysis And Infinite-dimensional Lie Groups -- Aspects Of Stochastic Global Analysis / K. D. Elworthy -- Lie Group Structure For Automorphisms Of A Contact Weyl Manifold / Naoya Miyazaki -- Pt. Ii. Riemannian Geometry -- Projective Structures Of A Curve In A Conformal Space / Osamu Kobayashi -- Deformations Of Surfaces Preserving Conformal Or Similarity Invariants / Atsushi Fujioka And Jun-ichi Inoguchi -- Global Structures Of Compact Conformally Flat Semi-symmetric Spaces Of Dimension 3 And Of Non-constant Curvature / Midori S. Goto -- Differential Geometry Of Analytic Surfaces With Singularities / Takao Sasai -- Pt. Iii. Symplectic Geometry And Poisson Geometry -- Integration Problem For Complex Lie Algebroids / Alan Weinstein -- Reduction, Induction And Ricci Flat Symplectic Connections / Michel Cahen And Simone Gutt -- Local Lie Algebra Determines Base Manifold / Janusz Grabowski -- Lie Algebroids Associated With Deformed Schouten Bracket Of 2-vector Fields / Kentaro Mikami And Tadayoshi Mizutani -- Parabolic Geometries Associated With Differential Equations Of Finite Type / Keizo Yamaguchi And Tomoaki Yatsui -- Pt. Iv. Quantizations And Noncommutative Geometry -- Toward Geometric Quantum Theory / Hideki Omori -- Resonance Gyrons And Quantum Geometry / Mikhail Karasev -- Secondary Invariant Of Foliated Spaces And Type Iii[subscript [gamma]] Von Neumann Algebras / Hitoshi Moriyoshi -- Geometry Of Space-time And Its Deformations : A Physical Perspective / Daniel Sternheimer -- Geometric Objects In An Approach To Quantum Geometry / Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki And Akira Yoshioka. Yoshiaki Maeda ... [et Al.], Editors. Includes Bibliographical References. 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 Contains invited expository articles by well-known mathematicians in differential geometry and mathematical physics. This work focuses on trends in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry Composed of invited articles in differential geometry and mathematical physics in honor of Hideki Omori. This title includes papers that focus on trends and future directions in symplectic and Poisson geometry, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry.