Connes, Alain

Conversations on mind, matter, and mathematics by Jean-Pierre Changeux ( Book )
23 editions published between 1989 and 2008 in 4 languages and held by 1,057 libraries worldwide
Les mathématiques et la biologie se trouvent aux deux extrémités du spectre de la science. D'un côté la rigueur logique, débarrassée de toute contingence matérielle, de l'autre une science d'observation, profondément tributaire de savoir-faire techniques et de concepts moraux. Ce livre d'entretiens tente de créer une passerelle entre ces disciplines que tout éloigne. Les deux auteurs, tous deux académiciens et professeurs au Collège de France, s'interrogent sur la nature de la pensée, l'existence des objets mathématiques ou le rapport entre le cerveau et les machines.

Noncommutative geometry by Alain Connes ( Book )
14 editions published between 1990 and 2008 in 3 languages and held by 519 libraries worldwide

On space and time ( Book )
6 editions published between 2008 and 2010 in English and held by 406 libraries worldwide
This volume brings together world leaders in cosmology, particle physics, quantum gravity, mathematics, philosophy and theology, to provide fresh insights into the deep structure of space and time. In one essay, Andrew Taylor explains the evidence for dark matter and dark energy.

Triangle of thoughts by Alain Connes ( Book )
12 editions published between 2000 and 2002 in English and French and held by 331 libraries worldwide
Ce dialogue entre trois mathématiciens offre une confrontation de trois points de vue sur les mathématiques et de trois pratiques de cette discipline. Le dialogue tourne autour de quatre thèmes : la nature des mathématiques, l'interprétation de la mécanique quantique et son unification avec la relativité, le temps mathématique et le temps humain.

Noncommutative geometry : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 3-9, 2000 ( Book )
7 editions published in 2004 in English and German and held by 306 libraries worldwide

Noncommutative geometry, quantum fields and motives by Alain Connes ( Book )
8 editions published between 2007 and 2008 in English and held by 287 libraries worldwide

Operator algebras, unitary representations, enveloping algebras, and invariant theory : actes du colloque en l'honneur de Jacques Dixmier ( Book )
6 editions published between 1990 and 1991 in English and French and held by 252 libraries worldwide

Symétries quantiques = Quantum symmetries : Les Houches, session LXIV, 1 Août - 8 Septembre 1995 ( Book )
2 editions published in 1998 in English and held by 109 libraries worldwide

Noncommutative geometry and global analysis : conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany ( Book )
1 edition published in 2011 in English and held by 94 libraries worldwide

Renormalization and Galois theories ( Book )
5 editions published in 2009 in English and held by 86 libraries worldwide
"This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics."--Publisher's description.