Edit Profile Connes, Alain Compute Distance To: Compute Author ID: connes.alain Published as: Connes, A.; Connes, Alain Homepage: http://www.alainconnes.org/en/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor Awards: Fields Medal (1982) · Clay Research Award (2000) Member of Collective: Bourbaki, Nicolas Documents Indexed: 270 Publications since 1969, including 21 Books Biographic References: 6 Publications all top 5 Co-Authors 106 single-authored 24 Consani, Caterina 21 Moscovici, Henri 18 Chamseddine, Ali Hani 14 Marcolli, Matilde 9 Kreimer, Dirk 7 Cuntz, Joachim 6 Gromov, Mikhael Leonidovich 6 Rieffel, Marc A. 5 Baum, Paul Frank 5 Dubois-Violette, Michel 4 Alon, Noga M. 4 Bourgain, Jean 4 Milman, Vitali D. 4 Størmer, Erling 4 van Suijlekom, Walter Daniël 4 Woods, Edward James 4 Yu, Guoliang 3 Changeux, Jean-Pierre 3 Jones, Vaughan Frederick Randal 3 Karoubi, Max 3 Sukochev, Fedor Anatol’evich 3 Takesaki, Masamichi 3 Zanin, Dmitriy V. 2 Bost, Jean-Benoît 2 Higson, Nigel 2 Lichnerowicz, Andre 2 Lott, John 2 Mcdonald, Edward A. 2 Ramachandran, Niranjan 2 Schützenberger, Marcel-Paul 2 Schwarz, Albert S. 2 Skandalis, Georges 2 Sullivan, Dennis Parnell 2 Teleman, Nicolae Sinel 2 Weiss, Benjamin 1 Atiyah, Michael Francis 1 Brezin, Eva 1 Brodskiĭ, Ya. S. 1 Damour, Thibault 1 Douglas, Michael R. 1 Duflo, Michel 1 Ellwood, David Alexandre 1 Evans, David E. 1 Fack, Thierry 1 Fathizadeh, Farzad 1 Fauvet, Frédéric 1 Fayet, Pierre 1 Feldman, Jacob 1 Flato, Moshé 1 Fröhlich, Jürg Martin 1 Gawȩdzki, Krzysztof 1 Gorokhovsky, Alexander 1 Haagerup, Uffe Valentin 1 Helffer, Bernard 1 Joseph, Anthony 1 Kouneiher, Joseph 1 Krieger, Wolfgang 1 Landi, Giovanni 1 Lebowitz, Joel Louis 1 Lesch, Matthias 1 Levitina, Galina 1 Mukhanov, Viatcheslav F. 1 Musat, Magdalena 1 Narnhofer, Heide 1 Nest, Ryszard 1 Pflaum, Markus J. 1 Ramis, Jean-Pierre 1 Rentschler, Rudolf 1 Rnagipour, Bahram 1 Rørdam, Mikael 1 Rovelli, Carlo 1 Schick, Thomas 1 Shlyakhtenko, Dimitri L. 1 Sternheimer, Daniel 1 Thirring, Walter E. 1 Tretkoff, Paula 1 Vaes, Stefaan 1 Van Daele, Alfons 1 Zagier, Don Bernard 1 Zinn-Justin, Jean all top 5 Serials 17 Communications in Mathematical Physics 13 Comptes Rendus de l’Académie des Sciences. Série I 12 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 9 Letters in Mathematical Physics 8 Journal of Geometry and Physics 7 Journal of Functional Analysis 7 Journal of High Energy Physics 7 Oberwolfach Reports 4 Journal of Number Theory 4 Ergodic Theory and Dynamical Systems 4 Selecta Mathematica. New Series 3 Journal of Mathematical Physics 3 Advances in Mathematics 3 Annals of Mathematics. Second Series 3 Physical Review Letters 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Bulletin of the London Mathematical Society 2 Tohoku Mathematical Journal. Second Series 2 Topology 2 Journal of Operator Theory 2 \(K\)-Theory 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Nuclear Physics, B, Proceedings Supplements 2 Moscow Mathematical Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Noncommutative Geometry 2 Modern Birkhäuser Classics 1 American Mathematical Monthly 1 Classical and Quantum Gravity 1 Israel Journal of Mathematics 1 Nuclear Physics. B 1 Fortschritte der Physik 1 Acta Mathematica 1 Acta Scientiarum Mathematicarum 1 Annales de l’Institut Fourier 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Canadian Mathematical Bulletin 1 Compositio Mathematica 1 Gazette des Mathématiciens 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Scandinavica 1 Nagoya Mathematical Journal 1 Pacific Journal of Mathematics 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti del Seminario Matematico della Università di Padova 1 Journal of the American Mathematical Society 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 IMRN. International Mathematics Research Notices 1 Elemente der Mathematik 1 L’Enseignement Mathématique. 2e Série 1 Journal of Algebraic Geometry 1 Journal de Théorie des Nombres de Bordeaux 1 Theory and Applications of Categories 1 Matematicheskaya Fizika, Analiz, Geometriya 1 Sbornik: Mathematics 1 European Mathematical Society Newsletter 1 Advances in Theoretical and Mathematical Physics 1 Annales Henri Poincaré 1 Journal of the Institute of Mathematics of Jussieu 1 International Journal of Geometric Methods in Modern Physics 1 Bulletin of the American Mathematical Society 1 Astérisque 1 Colloquium Publications. American Mathematical Society 1 Contemporary Mathematics 1 Progress in Mathematics 1 Texts and Readings in Mathematics 1 SMF Journée Annuelle 1 IRMA Lectures in Mathematics and Theoretical Physics 1 Münster Journal of Mathematics 1 Journal of \(K\)-Theory 1 Japanese Journal of Mathematics. 3rd Series 1 Higher Structures 1 Les Grandes Voix de la Recherche all top 5 Fields 147 Functional analysis (46-XX) 110 Global analysis, analysis on manifolds (58-XX) 70 Quantum theory (81-XX) 46 Number theory (11-XX) 31 \(K\)-theory (19-XX) 28 General and overarching topics; collections (00-XX) 28 Algebraic geometry (14-XX) 28 Associative rings and algebras (16-XX) 24 Manifolds and cell complexes (57-XX) 17 Category theory; homological algebra (18-XX) 14 Topological groups, Lie groups (22-XX) 14 Algebraic topology (55-XX) 13 Differential geometry (53-XX) 11 Nonassociative rings and algebras (17-XX) 11 Measure and integration (28-XX) 11 Relativity and gravitational theory (83-XX) 8 History and biography (01-XX) 8 Field theory and polynomials (12-XX) 6 Group theory and generalizations (20-XX) 6 Operator theory (47-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Geometry (51-XX) 4 Commutative algebra (13-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Mathematical logic and foundations (03-XX) 3 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 3 Biology and other natural sciences (92-XX) 2 Functions of a complex variable (30-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 221 Publications have been cited 9,333 times in 4,683 Documents Cited by ▼ Year ▼ Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076Connes, Alain 772 1994 Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042Connes, Alain 375 1976 Non-commutative differential geometry. Zbl 0592.46056Connes, Alain 336 1985 Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004Connes, A. 330 1987 Une classification des facteurs de type III. Zbl 0274.46050Connes, Alain 252 1973 Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009Connes, Alain 227 1996 On the foundations of noncommutative geometry. Zbl 1106.58004Connes, A. 218 2006 Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038Connes, Alain; Kreimer, Dirk 204 1998 Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem. Zbl 1032.81026Connes, Alain; Kreimer, Dirk 187 2000 The spectral action principle. Zbl 0894.58007Chamseddine, Ali H.; Connes, Alain 187 1997 The local index formula in noncommutative geometry. Zbl 0960.46048Connes, A.; Moscovici, H. 179 1995 Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052Connes, Alain; Douglas, Michael R.; Schwarz, Albert 178 1998 An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018Connes, A.; Feldman, J.; Weiss, B. 171 1981 Noncommutative geometry and reality. Zbl 0871.58008Connes, Alain 138 1995 Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061Baum, Paul; Connes, Alain; Higson, Nigel 121 1994 Gravity and the standard model with neutrino mixing. Zbl 1140.81022Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 120 2007 Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047Connes, Alain; Moscovici, Henri 119 1990 The longitudinal index theorem for foliations. Zbl 0575.58030Connes, A.; Skandalis, G. 119 1984 An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043Connes, A. 116 1981 Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005Connes, A.; Moscovici, H. 114 1998 Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040Bost, J.-B.; Connes, A. 109 1995 The flow of weights on factors of type III. Zbl 0408.46047Connes, Alain; Takesaki, Masamichi 106 1977 Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045Connes, Alain; Landi, Giovanni 105 2001 Non-commutative geometry and physics. Zbl 0933.46069Connes, A. 104 1995 Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052Connes, Alain 103 1975 The action functional in non-commutative geometry. Zbl 0658.53068Connes, A. 102 1988 Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059Connes, Alain; Kreimer, Dirk 100 2001 C* algèbres et géométrie différentielle. Zbl 0433.46057Connes, Alain 99 1980 Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009Connes, Alain 95 1983 Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051Connes, A. 94 1989 Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073Connes, A.; Narnhofer, H.; Thirring, W. 92 1987 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005Connes, Alain; Dubois-Violette, Michel 89 2002 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007Connes, Alain; Marcolli, Matilde 88 2008 A survey of foliations and operator algebras. Zbl 0531.57023Connes, A. 87 1982 Almost periodic states and factors of type III\(_1\). Zbl 0302.46050Connes, A. 85 1974 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015Connes, Alain 83 1999 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 81 2008 Property \(T\) for von Neumann algebras. Zbl 1190.46047Connes, A.; Jones, V. 78 1985 Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032Connes, Alain; Størmer, Erling 78 1975 On the spectral characterization of manifolds. Zbl 1287.58004Connes, Alain 73 2013 Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078Connes, Alain 67 1974 On the spatial theory of von Neumann algebras. Zbl 0443.46042Connes, A. 66 1980 Particle models and noncommutative geometry. Zbl 0957.46516Connes, Alain; Lott, John 65 1990 Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049Connes, A. 62 1988 Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505Chamseddine, Ali H.; Connes, Alain 60 1996 Deformations, asymptotic morphisms and bivariant \(K\)-theory. Zbl 0717.46062Connes, Alain; Higson, Nigel 59 1990 Sur la théorie non commutative de l’intégration. Zbl 0412.46053Connes, Alain 58 1979 Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086Connes, A.; Rovelli, C. 57 1994 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 53 2008 Geometry from the spectral point of view. Zbl 1042.46515Connes, Alain 52 1995 A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056Connes, A. 50 1980 Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027Connes, A. 49 1977 On the cohomology of operator algebras. Zbl 0408.46042Connes, A. 47 1978 Modular curvature for noncommutative two-tori. Zbl 1332.46070Connes, Alain; Moscovici, Henri 46 2014 Yang-Mills for non-commutative two-tori. Zbl 0633.46069Connes, Alain; Rieffel, Marc A. 46 1987 Property T and asymptotically invariant sequences. Zbl 0479.28017Connes, A.; Weiss, B. 46 1980 Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048Connes, Alain; Størmer, Erling 45 1978 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 44 2008 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 43 2011 Introduction to non commutative differential geometry. Zbl 0564.58002Connes, A. 42 1985 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 41 2004 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042Baum, Paul; Connes, Alain 41 2000 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 40 2010 The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031Connes, Alain; Moscovici, Henri 39 1982 Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054Connes, A. 37 1986 A short survey of noncommutative geometry. Zbl 0974.58008Connes, Alain 36 2000 Cyclic cohomology and Hopf algebras. Zbl 0941.16024Connes, Alain; Moscovici, Henri 35 1999 Closed star products and cyclic cohomology. Zbl 0767.55005Connes, Alain; Flato, Moshé; Sternheimer, Daniel 35 1992 A factor not anti-isomorphic to itself. Zbl 0315.46058Connes, A. 34 1975 Noncommutative geometry. Zbl 0745.46067Connes, Alain 33 1990 Chern character for discrete groups. Zbl 0656.55005Baum, Paul; Connes, Alain 32 1988 A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056Connes, A.; Jones, V. 32 1982 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 30 2011 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 29 2004 Yang-Mills algebra. Zbl 1028.53025Connes, Alain; Dubois-Violette, Michel 29 2002 Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013Connes, Alain; Krieger, Wolfgang 29 1977 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 28 2010 From physics to number theory via noncommutative geometry. Zbl 1126.58006Connes, Alain; Marcolli, Matilde 26 2006 Characteristic 1, entropy and the absolute point. Zbl 1273.11140Connes, Alain; Consani, Caterina 25 2011 Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067Connes, A.; Cuntz, J. 25 1988 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 24 2013 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 24 2012 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 24 2008 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 24 2007 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 24 2001 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006Connes, Alain; Moscovici, Henri 24 2000 Scale invariance in the spectral action. Zbl 1112.83036Chamseddine, Ali H.; Connes, Alain 23 2006 KMS states and complex multiplication. Zbl 1106.58005Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 23 2005 Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006Connes, Alain; Moscovici, Henri 23 1993 Approximately transitive flows and ITPFI factors. Zbl 0606.46041Connes, A.; Woods, E. J. 23 1985 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 22 2007 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034Connes, Alain; Shlyakhtenko, Dimitri 22 2005 The metric aspect of noncommutative geometry. Zbl 1221.58007Connes, Alain; Lott, John 22 1992 Sur la classification des facteurs de type II. Zbl 0304.46042Connes, Alain 22 1975 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 21 2011 Fun with \(\mathbb F_1\). Zbl 1228.11143Connes, Alain; Consani, Caterina; Marcolli, Matilde 21 2009 Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069Connes, A.; Gromov, M.; Moscovici, H. 21 1993 Classification des facteurs. Zbl 0503.46043Connes, A. 21 1982 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 20 2010 Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023Connes, Alain; Moscovici, Henri 20 2004 Entropy and the spectral action. Zbl 1444.46049Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 1 2020 The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008Connes, Alain; Fathizadeh, Farzad 6 2019 Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D. 6 2019 Homological algebra in characteristic one. Zbl 1411.18006Connes, Alain; Consani, Caterina 4 2019 Noncommutative geometry for symmetric non-self-adjoint operators. Zbl 07063161Connes, Alain; Levitina, Galina; McDonald, Edward; Sukochev, Fedor; Zanin, Dmitriy 2 2019 Geometry and the quantum. Zbl 1411.58003Connes, Alain 1 2018 Geometry of the scaling site. Zbl 1406.11118Connes, Alain; Consani, Caterina 7 2017 Trace theorem for quasi-Fuchsian groups. Zbl 06842855Connes, Alain; Sukochev, Fedor A.; Zanin, Dmitriy V. 5 2017 Geometry of the arithmetic site. Zbl 1368.14038Connes, Alain; Consani, Caterina 14 2016 Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046Connes, Alain; Consani, Caterina 6 2016 An essay on the Riemann hypothesis. Zbl 1353.11095Connes, Alain 5 2016 The scaling site. Zbl 1348.18004Connes, Alain; Consani, Caterina 5 2016 Grand unification in the spectral Pati-Salam model. Zbl 1388.81965Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 15 2015 Universal thickening of the field of real numbers. Zbl 1387.11086Connes, Alain; Consani, Caterina 13 2015 Projective geometry in characteristic one and the epicyclic category. Zbl 1338.19004Connes, Alain; Consani, Caterina 7 2015 Cyclic structures and the topos of simplicial sets. Zbl 1328.19005Connes, Alain; Consani, Caterina 6 2015 The cyclic and epicyclic sites. Zbl 1331.18005Connes, Alain; Consani, Caterina 2 2015 Modular curvature for noncommutative two-tori. Zbl 1332.46070Connes, Alain; Moscovici, Henri 46 2014 The arithmetic site. Zbl 1315.11054Connes, Alain; Consani, Caterina 19 2014 Geometry and the quantum: basics. Zbl 1333.81414Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav 13 2014 On the arithmetic of the BC-system. Zbl 1302.11069Connes, Alain; Consani, Caterina 7 2014 Cyclic homology, Serre’s local factors and \(\lambda\)-operations. Zbl 1327.14109Connes, Alain; Consani, Caterina 6 2014 On the spectral characterization of manifolds. Zbl 1287.58004Connes, Alain 73 2013 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 24 2013 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 17 2013 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 24 2012 Spectral action for Robertson-Walker metrics. Zbl 1397.81413Chamseddine, Ali H.; Connes, Alain 14 2012 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 43 2011 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 30 2011 Characteristic 1, entropy and the absolute point. Zbl 1273.11140Connes, Alain; Consani, Caterina 25 2011 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 21 2011 The Witt construction in characteristic one and quantization. Zbl 1245.13015Connes, Alain 8 2011 Noncommutative geometric spaces with boundary: spectral action. Zbl 1209.53061Chamseddine, Ali H.; Connes, Alain 2 2011 The BC-system and \(L\)-functions. Zbl 1276.14002Connes, Alain 1 2011 Noncommutative geometry and global analysis. Conference in honor of Henri Moscovici, Bonn, Germany, June 29–July 4, 2009. Zbl 1218.00012Connes, Alain (ed.); Gorokhovsky, Alexander (ed.); Lesch, Matthias (ed.); Pflaum, Markus (ed.); Rnagipour, Bahram (ed.) 1 2011 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 40 2010 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 28 2010 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 20 2010 The uncanny precision of the spectral action. Zbl 1192.58005Chamseddine, Ali H.; Connes, Alain 17 2010 Visions in mathematics. GAFA 2000 special volume, Part II. Proceedings of the meeting “Visions in Mathematics – Towards 2000, Tel Aviv, Israel, August 25–September 3, 1999. Special volume of the journal Geometric and Functional Analysis – GAFA. Reprint of the 2000 original. Zbl 1185.00038Alon, Noga (ed.); Bourgain, Jean (ed.); Connes, Alain (ed.); Gromov, Mikhael (ed.); Milman, Vitali D. (ed.) 1 2010 Fun with \(\mathbb F_1\). Zbl 1228.11143Connes, Alain; Consani, Caterina; Marcolli, Matilde 21 2009 The Weil proof and the geometry of the adelès class space. Zbl 1208.11108Connes, Alain; Consani, Caterina; Marcolli, Matilde 13 2009 Renormalization and Galois theories. Selected papers of the CIRM workshop, Luminy, France, March 2006. Zbl 1173.14003Connes, Alain (ed.); Fauvet, Frédéric (ed.); Ramis, Jean-Pierre (ed.) 1 2009 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007Connes, Alain; Marcolli, Matilde 88 2008 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 81 2008 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 53 2008 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 44 2008 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 24 2008 Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres. Zbl 1159.58003Connes, Alain; Dubois-Violette, Michel 10 2008 A unitary invariant in Riemannian geometry. Zbl 1197.46030Connes, Alain 5 2008 Gravity and the standard model with neutrino mixing. Zbl 1140.81022Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 120 2007 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 24 2007 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 22 2007 Quantum gravity boundary terms from the spectral action of noncommutative space. Zbl 1228.83080Chamseddine, Ali H.; Connes, Alain 17 2007 Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory. Zbl 1200.81113Connes, Alain; Marcolli, Matilde 16 2007 Yang-Mills and some related algebras. Zbl 1177.58009Connes, Alain; Dubois-Violette, Michel 10 2007 A property of parallelograms inscribed in ellipses. Zbl 1140.51010Connes, Alain; Zagier, Don 4 2007 Noncommutative geometry. Abstracts from the workshop held September 2–8, 2007. Zbl 1177.58003Connes, Alain (ed.); Cuntz, Joachim (ed.); Rieffel, Marc A. (ed.) 1 2007 On the foundations of noncommutative geometry. Zbl 1106.58004Connes, A. 218 2006 From physics to number theory via noncommutative geometry. Zbl 1126.58006Connes, Alain; Marcolli, Matilde 26 2006 Scale invariance in the spectral action. Zbl 1112.83036Chamseddine, Ali H.; Connes, Alain 23 2006 Inner fluctuations of the spectral action. Zbl 1105.58004Connes, Alain; Chamseddine, Ali H. 17 2006 Quantum fields and motives. Zbl 1092.81050Connes, Alain; Marcolli, Matilde 13 2006 Noncommutative geometry and physics. Zbl 1129.83012Connes, Alain 8 2006 KMS states and complex multiplication. II. Zbl 1123.58004Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 8 2006 \(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. Zbl 1139.58003Connes, Alain; Marcolli, Matilde 6 2006 Transgressions of the Godbillon-Vey class and Rademacher functions. Zbl 1109.11027Connes, Alain; Moscovici, Henri 1 2006 KMS states and complex multiplication. Zbl 1106.58005Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 23 2005 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034Connes, Alain; Shlyakhtenko, Dimitri 22 2005 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 41 2004 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 29 2004 Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023Connes, Alain; Moscovici, Henri 20 2004 Renormalization and motivic Galois theory. Zbl 1131.81021Connes, Alain; Marcolli, Matilde 10 2004 Cyclic cohomology, noncommutative geometry and quantum group symmetries. Zbl 1052.46057Connes, Alain 5 2004 Moduli space and structure of noncommutative 3-spheres. Zbl 1052.58012Connes, Alain; Dubois-Violette, Michel 16 2003 Galois symmetries and renormalization. Zbl 1050.81052Connes, Alain 1 2003 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005Connes, Alain; Dubois-Violette, Michel 89 2002 Yang-Mills algebra. Zbl 1028.53025Connes, Alain; Dubois-Violette, Michel 29 2002 Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Zbl 1033.81061Connes, A.; Kreimer, D. 16 2002 Noncommutative geometry year 2000. Zbl 1138.58304Connes, Alain 6 2002 Hommage à Laurent Schwartz. Zbl 1015.01013Connes, Alain 1 2002 Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045Connes, Alain; Landi, Giovanni 105 2001 Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059Connes, Alain; Kreimer, Dirk 100 2001 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 24 2001 From local perturbation theory to Hopf- and Lie-algebras of Feynman graphs. Zbl 1015.81042Connes, A.; Kreimer, D. 4 2001 Triangle of thoughts. Translated from the French by Jennifer Gage. Zbl 1015.00005Connes, Alain; Lichnerowicz, André; Schützenberger, Marcel Paul 4 2001 From local perturbation theory to Hopf and Lie algebras of Feynman graphs. Zbl 0995.81077Connes, Alain; Kreimer, Dirk 4 2001 Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem. Zbl 1032.81026Connes, Alain; Kreimer, Dirk 187 2000 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042Baum, Paul; Connes, Alain 41 2000 A short survey of noncommutative geometry. Zbl 0974.58008Connes, Alain 36 2000 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006Connes, Alain; Moscovici, Henri 24 2000 Noncommutative geometry year 2000. Zbl 0985.58003Connes, Alain 15 2000 Noncommutative geometry and the Riemann zeta function. Zbl 0960.11042Connes, Alain 3 2000 Cyclic cohomology and Hopf algebra symmetry. Zbl 0970.58005Connes, Alain; Moscovici, Henri 2 2000 GAFA 2000. Visions in mathematics—Towards 2000. Proceedings of a meeting, Tel Aviv, Israel, August 25–September 3, 1999. Part II. Special volume of the journal Geometric and Functional Analysis. Zbl 0960.00035Alon, N. (ed.); Bourgain, Jean (ed.); Connes, A. (ed.); Gromov, M. (ed.); Milman, V. (ed.) 1 2000 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015Connes, Alain 83 1999 Cyclic cohomology and Hopf algebras. Zbl 0941.16024Connes, Alain; Moscovici, Henri 35 1999 Renormalization in quantum field theory and the Riemann-Hilbert problem. Zbl 0957.81011Connes, Alain; Kreimer, Dirk 11 1999 Hopf algebras, renormalization and noncommutative geometry. Zbl 1041.81086Connes, A.; Kreimer, D. 8 1999 Lessons from quantum field theory: Hopf algebras and spacetime geometries. Zbl 0965.81046Connes, Alain; Kreimer, Dirk 8 1999 ...and 121 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,430 Authors 82 Connes, Alain 50 Marcolli, Matilde 49 Sukochev, Fedor Anatol’evich 43 Guo, Li 42 Popa, Sorin Teodor 33 van Suijlekom, Walter Daniël 31 Landi, Giovanni 31 Rennie, Adam 29 Iochum, Bruno 29 Sitarz, Andrzej 28 Carey, Alan L. 28 Khalkhali, Masoud 27 Longo, Roberto 26 Dabrowski, Ludwik 26 Vaes, Stefaan 25 Houdayer, Cyril 25 Majid, Shahn 25 Martinetti, Pierre 23 Haagerup, Uffe Valentin 23 Lizzi, Fedele 23 Ponge, Raphaël S. 23 Skandalis, Georges 22 Ebrahimi-Fard, Kurusch 22 Neshveyev, Sergey V. 21 Chamseddine, Ali Hani 21 Golodets, Valentin Yakovlevich 21 Ioana, Adrian 21 Wulkenhaar, Raimar 21 Yu, Guoliang 20 Benameur, Moulay-Tahar 20 Consani, Caterina 20 Zanin, Dmitriy V. 19 Dubois-Violette, Michel 19 Goswami, Debashish 19 Jørgensen, Palle E. T. 19 Laca, Marcelo 19 Mathai, Varghese 19 Narnhofer, Heide 19 Schücker, Thomas 18 D’Andrea, Francesco 18 Wang, Yong 17 Bai, Chengming 17 Brzeziński, Tomasz 17 Moscovici, Henri 17 Nest, Ryszard 17 Rangipour, Bahram 17 Størmer, Erling 16 Foissy, Loïc 16 Kaad, Jens 15 Chakraborty, Partha Sarathi 15 Cho, Ilwoo 15 Choda, Marie 15 Elliott, George A. 15 Gao, Xing 15 Manchon, Dominique 15 Takesaki, Masamichi 15 Wallet, Jean-Christophe 14 Bhowmick, Jyotishman 14 Cuntz, Joachim 14 Fathizadeh, Farzad 14 Gracia-Bondía, José M. 14 Lorscheid, Oliver 14 Nistor, Victor 14 Stephan, Christoph A. 14 Thomsen, Klaus E. 14 Voiculescu, Dan-Virgil 13 Chifan, Ionuţ 13 Christensen, Erik 13 Dadarlat, Marius 13 Junge, Marius 13 Klimek, Slawomir 13 Latrémolière, Frédéric 13 Lesniewski, Andrzej 13 Patras, Frédéric 13 Schulz-Baldes, Hermann 13 Tang, Xiang 13 Várilly, Joseph C. 12 Bellissard, Jean V. 12 Gayral, Victor 12 Grosse, Harald 12 Iovane, Gerardo 12 Jones, Vaughan Frederick Randal 12 Kishimoto, Akitaka 12 Masson, Thierry 12 Masuda, Toshihiko 12 Meyer, Ralf 12 Paycha, Sylvie 12 Schrohe, Elmar 12 Tomatsu, Reiji 11 Aastrup, Johannes 11 Bieliavsky, Pierre 11 Fidaleo, Francesco 11 Giordano, Thierry 11 Heller, Michał P. 11 Kastler, Daniel 11 Kellendonk, Johannes 11 Larsen, Nadia S. 11 Lesch, Matthias 11 Phillips, N. Christopher 11 Raeburn, Iain ...and 3,330 more Authors all top 5 Cited in 358 Serials 394 Journal of Functional Analysis 303 Communications in Mathematical Physics 233 Journal of Geometry and Physics 181 Journal of Mathematical Physics 181 Advances in Mathematics 146 Letters in Mathematical Physics 142 Journal of Noncommutative Geometry 139 Nuclear Physics. B 105 Proceedings of the American Mathematical Society 96 Transactions of the American Mathematical Society 90 Journal of High Energy Physics 75 \(K\)-Theory 68 Journal of Algebra 68 Journal of Pure and Applied Algebra 62 Mathematische Annalen 60 Publications of the Research Institute for Mathematical Sciences, Kyoto University 58 Ergodic Theory and Dynamical Systems 57 Inventiones Mathematicae 54 Comptes Rendus. Mathématique. Académie des Sciences, Paris 50 Journal of Mathematical Analysis and Applications 50 Physics Letters. B 50 International Journal of Mathematics 48 International Journal of Modern Physics A 47 International Journal of Geometric Methods in Modern Physics 45 International Journal of Theoretical Physics 45 Reviews in Mathematical Physics 40 Chaos, Solitons and Fractals 38 Journal für die Reine und Angewandte Mathematik 34 Israel Journal of Mathematics 32 Journal of \(K\)-Theory 28 Communications in Algebra 27 Bulletin of the American Mathematical Society. New Series 25 Annales de l’Institut Fourier 24 Reports on Mathematical Physics 23 Journal of Number Theory 23 Annales Henri Poincaré 22 General Relativity and Gravitation 22 Acta Mathematica 22 Integral Equations and Operator Theory 21 Rocky Mountain Journal of Mathematics 20 Modern Physics Letters A 20 Duke Mathematical Journal 20 Geometric and Functional Analysis. GAFA 20 Journal of Mathematical Sciences (New York) 19 SIGMA. 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Physique Théorique 9 Annales Mathématiques Blaise Pascal 9 Geometry & Topology 9 Algebras and Representation Theory 9 Physical Review Letters 9 Journal of Homotopy and Related Structures 8 Geometriae Dedicata 8 Differential Geometry and its Applications 8 Proceedings of the National Academy of Sciences of the United States of America 8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 8 Annals of Mathematics. Second Series 7 Archiv der Mathematik ...and 258 more Serials all top 5 Cited in 61 Fields 2,169 Functional analysis (46-XX) 1,299 Quantum theory (81-XX) 945 Global analysis, analysis on manifolds (58-XX) 554 Associative rings and algebras (16-XX) 443 \(K\)-theory (19-XX) 391 Operator theory (47-XX) 379 Topological groups, Lie groups (22-XX) 364 Differential geometry (53-XX) 338 Nonassociative rings and algebras (17-XX) 324 Relativity and gravitational theory (83-XX) 307 Dynamical systems and ergodic theory (37-XX) 271 Group theory and generalizations (20-XX) 246 Category theory; homological algebra (18-XX) 234 Number theory (11-XX) 196 Algebraic geometry (14-XX) 193 Manifolds and cell complexes (57-XX) 163 Measure and integration (28-XX) 161 Combinatorics (05-XX) 157 Algebraic topology (55-XX) 148 Statistical mechanics, structure of matter (82-XX) 119 Abstract harmonic analysis (43-XX) 96 Probability theory and stochastic processes (60-XX) 89 Partial differential equations (35-XX) 61 Commutative algebra (13-XX) 55 Mathematical logic and foundations (03-XX) 55 Several complex variables and analytic spaces (32-XX) 52 Linear and multilinear algebra; matrix theory (15-XX) 52 General topology (54-XX) 45 Order, lattices, ordered algebraic structures (06-XX) 44 Information and communication theory, circuits (94-XX) 36 Ordinary differential equations (34-XX) 34 Field theory and polynomials (12-XX) 31 Functions of a complex variable (30-XX) 31 Computer science (68-XX) 30 Convex and discrete geometry (52-XX) 28 Harmonic analysis on Euclidean spaces (42-XX) 28 Mechanics of particles and systems (70-XX) 25 Geometry (51-XX) 24 General and overarching topics; collections (00-XX) 19 Special functions (33-XX) 17 Numerical analysis (65-XX) 14 General algebraic systems (08-XX) 13 History and biography (01-XX) 10 Real functions (26-XX) 10 Statistics (62-XX) 9 Optics, electromagnetic theory (78-XX) 9 Classical thermodynamics, heat transfer (80-XX) 9 Operations research, mathematical programming (90-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Astronomy and astrophysics (85-XX) 7 Difference and functional equations (39-XX) 6 Potential theory (31-XX) 6 Sequences, series, summability (40-XX) 6 Approximations and expansions (41-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Systems theory; control (93-XX) 5 Integral transforms, operational calculus (44-XX) 3 Integral equations (45-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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