Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation...
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of fol...
This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in...
This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory u...
Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a...
Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathemat...
Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in...
Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties b...
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics; for example, Floer theory has contributed new insights to quantum field theory. In a related direction, noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more...
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic top...
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation...
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of fol...
The book contains a collection of the lectures and talks presented in the Tohoku Forum for Creativity, based on the program of the thematic year in the period of 2014-2016.The main subjects are Noncommutative Geometry and String Theory, including Quantum Field Theory, Poisson Geometry and Deformation Quantization. This book gives an overview of the recent developments in these subjects and thus, to simulate the exchange at new ideas between mathematicians and physicists.
The book contains a collection of the lectures and talks presented in the Tohoku Forum for Creativity, based on the program of the thematic year in th...
This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi's career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kahler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the...
This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to ...
