"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. Th ..."
"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. Th ..."
"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 mathematicia ..."
"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 mathematicia ..."
"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 pres ..."
"Math. Phys. 249 (2004) 383 [hep-th/0306062]. P. Bouwknegt, K. Hannabuss and
V. Mathai, T-duality for principal torus bundles and dimensionally reduced Gysin
sequences, Adv. Theor. Math. Phys. 9 (2005) 749 [hep-th/0412268]. P.
Bouwknegt, Lectures on cohomology, T-duality, and generalized geometry, Lect.
Notes Phys. 807 (2010) 261. R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn
and F. Rennecke, Non-geometric Fluxes, Asymmetric Stri ..."
"... Ansgar Schneider, Die lokale Struktur von T-Dualitätstripeln (the local structure
of T-duality triples), Ph.D. thesis, Universität Göttingen, 2007, arXiv.org:
0712.0260. A. Sen, An introduction to duality symmetries in string theory, Unity
from duality: gravity, gauge theory and strings (Les Houches, 2001), NATO Adv.
Study Inst., EDP Sci., Les Ulis, 2003, pp. 241–322. MR2010972 (2004i:81208)
Andrew Strominger, Shing-Tung Yau, a ..."
"Proceedings of the Workshop at Shonan, Japan, June 1999 Yoshiaki Maeda,
Hitoshi Moriyoshi, Hideki Omori, Daniel Sternheimer, Tatsuya Tate, Satoshi
Watamura. Set F(0) = f°. erte"dt. ... be written as —ió.(x), for £e"dt means the
Fourier transform of 1 in the *-product. Though the delta function 6(a) is not a
genuine function of a, J.: e"dt is a genuine function of x in the -product. Indeed
this is given as #Jo(#4), by using Hansen-B ..."
"Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space-time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address th ..."
"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 ..."
"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 bet ..."