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 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...

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.