Edit Profile (opens in new tab) Connes, Alain Co-Author Distance Author ID: connes.alain Published as: Connes, Alain; Connes, A. Homepage: https://alainconnes.org/ External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr Awards: Fields Medal (1982) · Clay Research Award (2000) Member of Collective: Bourbaki, Nicolas Documents Indexed: 283 Publications since 1969, including 12 Books and 15 Additional arXiv Preprints 21 Contributions as Editor · 6 Further Contributions Biographic References: 7 Publications Co-Authors: 88 Co-Authors with 195 Joint Publications 3,352 Co-Co-Authors all top 5 Co-Authors 113 single-authored 40 Consani, Caterina 27 Moscovici, Henri 19 Chamseddine, Ali Hani 16 Marcolli, Matilde 9 Kreimer, Dirk 7 Cuntz, Joachim 7 Yu, Guoliang 6 Baum, Paul Frank 6 Gromov, Mikhael Leonidovich 6 Rieffel, Marc A. 6 van Suijlekom, Walter Daniël 5 Dubois-Violette, Michel 4 Alon, Noga 4 Bourgain, Jean 4 Milman, Vitali D. 4 Størmer, Erling 4 Woods, Edward James 3 Changeux, Jean-Pierre 3 Evans, David E. 3 Jones, Vaughan Frederick Randal 3 Karoubi, Max 3 Nest, Ryszard 3 Skandalis, Georges 3 Sukochev, Fedor Anatol’evich 3 Takesaki, Masamichi 3 Zanin, Dmitriy V. 2 Bost, Jean-Benoît 2 Douglas, Michael R. 2 Haagerup, Uffe Valentin 2 Higson, Nigel 2 Jaffe, Arthur Michael 2 Lichnerowicz, Andre 2 Lott, John 2 McDonald, Edward Andrew 2 Mukhanov, Viatcheslav F. 2 Narnhofer, Heide 2 Nikolaus, Thomas 2 Ramachandran, Niranjan 2 Schützenberger, Marcel-Paul 2 Schwarz, Albert S. 2 Shlyakhtenko, Dimitri L. 2 Sullivan, Dennis Parnell 2 Teleman, Nicolae Sinel 2 Weiss, Benjamin 1 Atiyah, Michael Francis 1 Barnsley, Michael Fielding 1 Baxter, Rodney J. 1 Birman, Joan S. 1 Bisch, Dietmar H. 1 Blum, Lenore 1 Bowen, Ray M. 1 Brézin, Edouard 1 Brown, Larry 1 Bryant, Robert L. 1 Burns, Daniel M. jun. 1 Caramello, Olivia 1 Cartier, Pierre 1 Cheeger, Jeff 1 Coburn, Lewis A. 1 Conder, Marston Donald Edward 1 Damour, Thibault 1 de la Harpe, Pierre 1 Dehen, Michele 1 Donnelly, Harold 1 Duflo, Michel 1 Dundas, Bjørn Ian 1 Ebin, David G. 1 Ellwood, David Alexandre 1 Fack, Thierry 1 Fathizadeh, Farzad 1 Fauvet, Frédéric 1 Fayet, Pierre 1 Feldman, Jacob 1 Flato, Moshé 1 Freedman, Michael Hartley 1 Fröhlich, Jürg Martin 1 Gallavotti, Giovanni M. 1 Gawȩdzki, Krzysztof 1 Glashow, Sheldon Lee 1 Goodman, Fred J. 1 Gorokhovsky, Alexander 1 Griffiths, Phillip Augustus 1 Guillemin, Victor W. 1 Guionnet, Alice 1 Helffer, Bernard 1 Helton, John William 1 Howe, Roger Evans 1 Hutchins, Shana 1 Izumi, Masaki 1 Jaeck, Frédéric 1 Jørgensen, Palle E. T. 1 Joseph, Anthony 1 Kaminker, Jerome 1 Kawahigashi, Yasuyuki 1 Khalkhali, Masoud 1 Kirby, Robion Cromwell 1 Kishimoto, Aki 1 Kouneiher, Joseph 1 Krieger, Wolfgang 1 Lafforgue, Laurent ...and 55 more Co-Authors all top 5 Serials 18 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 9 Oberwolfach Reports 8 Journal of Geometry and Physics 7 Journal of Functional Analysis 7 Journal of High Energy Physics 6 Notices of the American Mathematical Society 5 Journal of Number Theory 5 Selecta Mathematica. New Series 4 Advances in Mathematics 4 Ergodic Theory and Dynamical Systems 3 Journal of Mathematical Physics 3 Journal of Operator Theory 3 Annals of Mathematics. Second Series 3 Physical Review Letters 2 Acta Scientiarum Mathematicarum 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Bulletin of the London Mathematical Society 2 Tôhoku Mathematical Journal. Second Series 2 Topology 2 \(K\)-Theory 2 Geometric and Functional Analysis. GAFA 2 L’Enseignement Mathématique. 2e Série 2 Bulletin of the American Mathematical Society. New Series 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 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 Journal of Algebraic Geometry 1 Journal de Théorie des Nombres de Bordeaux 1 Bulletin des Sciences Mathématiques 1 Theory and Applications of Categories 1 Matematicheskaya Fizika, Analiz, Geometriya 1 Sbornik: Mathematics 1 Documenta Mathematica 1 European Mathematical Society Newsletter 1 Advances in Theoretical and Mathematical Physics 1 Annales Henri Poincaré 1 The Quarterly Journal of Mathematics 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 Proceedings of Symposia in Pure Mathematics 1 Progress in Mathematics 1 Texts and Readings in Mathematics 1 SMF Journée Annuelle 1 IRMA Lectures in Mathematics and Theoretical Physics 1 Journal of Mathematics and Music 1 Münster Journal of Mathematics 1 Journal of \(K\)-Theory 1 Japanese Journal of Mathematics. 3rd Series 1 EMS Surveys in Mathematical Sciences 1 Higher Structures 1 Les Grandes Voix de la Recherche 1 Nouvelles Visions des Sciences all top 5 Fields 162 Functional analysis (46-XX) 123 Global analysis, analysis on manifolds (58-XX) 75 Quantum theory (81-XX) 64 Number theory (11-XX) 41 \(K\)-theory (19-XX) 38 Algebraic geometry (14-XX) 34 General and overarching topics; collections (00-XX) 31 Associative rings and algebras (16-XX) 25 Manifolds and cell complexes (57-XX) 24 Category theory; homological algebra (18-XX) 16 Topological groups, Lie groups (22-XX) 15 Algebraic topology (55-XX) 14 History and biography (01-XX) 12 Differential geometry (53-XX) 12 Relativity and gravitational theory (83-XX) 11 Nonassociative rings and algebras (17-XX) 11 Measure and integration (28-XX) 9 Operator theory (47-XX) 8 Field theory and polynomials (12-XX) 8 Group theory and generalizations (20-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Commutative algebra (13-XX) 5 Ordinary differential equations (34-XX) 5 Geometry (51-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Mathematical logic and foundations (03-XX) 3 Real functions (26-XX) 3 Biology and other natural sciences (92-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-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 Open 241 Publications have been cited 10,860 times in 5,663 Documents Cited by ▼ Year ▼ Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076 Connes, Alain 804 1994 Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042 Connes, Alain 424 1976 Non-commutative differential geometry. Zbl 0592.46056 Connes, Alain 352 1985 Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004 Connes, A. 317 1987 Une classification des facteurs de type III. Zbl 0274.46050 Connes, Alain 294 1973 Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem. Zbl 1032.81026 Connes, Alain; Kreimer, Dirk 281 2000 Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038 Connes, Alain; Kreimer, Dirk 273 1998 Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009 Connes, Alain 266 1996 On the foundations of noncommutative geometry. Zbl 1106.58004 Connes, A. 222 2006 The spectral action principle. Zbl 0894.58007 Chamseddine, Ali H.; Connes, Alain 218 1997 The local index formula in noncommutative geometry. Zbl 0960.46048 Connes, A.; Moscovici, H. 213 1995 An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018 Connes, A.; Feldman, J.; Weiss, B. 207 1981 Noncommutative geometry and reality. Zbl 0871.58008 Connes, Alain 181 1995 Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061 Baum, Paul; Connes, Alain; Higson, Nigel 163 1994 Gravity and the standard model with neutrino mixing. Zbl 1140.81022 Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 149 2007 The longitudinal index theorem for foliations. Zbl 0575.58030 Connes, A.; Skandalis, G. 147 1984 Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047 Connes, Alain; Moscovici, Henri 146 1990 An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043 Connes, A. 132 1981 The action functional in non-commutative geometry. Zbl 0658.53068 Connes, A. 131 1988 Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051 Connes, A. 131 1989 Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005 Connes, A.; Moscovici, H. 129 1998 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007 Connes, Alain; Marcolli, Matilde 128 2008 Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040 Bost, J.-B.; Connes, A. 127 1995 Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045 Connes, Alain; Landi, Giovanni 121 2001 Non-commutative geometry and physics. Zbl 0933.46069 Connes, A. 120 1995 Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059 Connes, Alain; Kreimer, Dirk 119 2001 Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052 Connes, Alain 119 1975 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015 Connes, Alain 112 1999 The flow of weights on factors of type III. Zbl 0408.46047 Connes, Alain; Takesaki, Masamichi 112 1977 C* algèbres et géométrie différentielle. Zbl 0433.46057 Connes, Alain 112 1980 Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009 Connes, Alain 111 1983 Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052 Connes, Alain; Douglas, Michael R.; Schwarz, Albert 107 1998 Property \(T\) for von Neumann algebras. Zbl 1190.46047 Connes, A.; Jones, V. 105 1985 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005 Connes, Alain; Dubois-Violette, Michel 102 2002 Almost periodic states and factors of type III\(_1\). Zbl 0302.46050 Connes, A. 99 1974 On the spectral characterization of manifolds. Zbl 1287.58004 Connes, Alain 98 2013 Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073 Connes, A.; Narnhofer, H.; Thirring, W. 97 1987 A survey of foliations and operator algebras. Zbl 0531.57023 Connes, A. 92 1982 Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032 Connes, Alain; Størmer, Erling 83 1975 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004 Connes, Alain; Marcolli, Matilde 83 2008 On the spatial theory of von Neumann algebras. Zbl 0443.46042 Connes, A. 81 1980 Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086 Connes, A.; Rovelli, C. 76 1994 Particle models and noncommutative geometry. Zbl 0957.46516 Connes, Alain; Lott, John 75 1990 Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505 Chamseddine, Ali H.; Connes, Alain 74 1996 Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078 Connes, Alain 73 1974 Deformations, asymptotic morphisms and bivariant \(K\)-theory. (Déformations, morphismes asymptotiques et \(K\)-théorie bivariante.) Zbl 0717.46062 Connes, Alain; Higson, Nigel 71 1990 Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049 Connes, A. 68 1988 Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027 Connes, A. 63 1977 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001 Connes, Alain; Consani, Caterina 62 2010 Property T and asymptotically invariant sequences. Zbl 0479.28017 Connes, A.; Weiss, B. 61 1980 Why the standard model. Zbl 1140.81021 Chamseddine, Ali H.; Connes, Alain 59 2008 Geometry from the spectral point of view. Zbl 1042.46515 Connes, Alain 59 1995 Modular curvature for noncommutative two-tori. Zbl 1332.46070 Connes, Alain; Moscovici, Henri 59 2014 Sur la théorie non commutative de l’intégration. Zbl 0412.46053 Connes, Alain 58 1979 Type III and spectral triples. Zbl 1159.46041 Connes, Alain; Moscovici, Henri 57 2008 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037 Connes, Alain; Tretkoff, Paula 54 2011 On the cohomology of operator algebras. Zbl 0408.46042 Connes, A. 54 1978 A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056 Connes, A. 52 1980 Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048 Connes, Alain; Størmer, Erling 51 1978 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012 Connes, Alain 46 2004 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042 Baum, Paul; Connes, Alain 45 2000 The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031 Connes, Alain; Moscovici, Henri 44 1982 Introduction to non commutative differential geometry. Zbl 0564.58002 Connes, A. 44 1985 Yang-Mills for non-commutative two-tori. Zbl 0633.46069 Connes, Alain; Rieffel, Marc A. 43 1987 The hyperring of adèle classes. Zbl 1221.14002 Connes, Alain; Consani, Caterina 43 2011 Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054 Connes, A. 40 1986 A factor not anti-isomorphic to itself. Zbl 0315.46058 Connes, A. 40 1975 Cyclic cohomology and Hopf algebras. Zbl 0941.16024 Connes, Alain; Moscovici, Henri 39 1999 A short survey of noncommutative geometry. Zbl 0974.58008 Connes, Alain 39 2000 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032 Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 39 2013 Closed star products and cyclic cohomology. Zbl 0767.55005 Connes, Alain; Flato, Moshé; Sternheimer, Daniel 38 1992 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024 Connes, Alain; Moscovici, Henri 36 2004 Noncommutative geometry. (Géométrie non commutative.) Zbl 0745.46067 Connes, Alain 35 1990 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130 Chamseddine, Ali H.; Connes, Alain 35 2010 Resilience of the spectral standard model. Zbl 1397.81412 Chamseddine, Ali H.; Connes, Alain 34 2012 A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056 Connes, A.; Jones, V. 33 1982 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014 Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 33 2013 Quantized calculus and applications. Zbl 1052.46510 Connes, Alain 32 1995 Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013 Connes, Alain; Krieger, Wolfgang 32 1977 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002 Connes, Alain; Consani, Caterina 31 2010 Yang-Mills algebra. Zbl 1028.53025 Connes, Alain; Dubois-Violette, Michel 31 2002 Chern character for discrete groups. Zbl 0656.55005 Baum, Paul; Connes, Alain 30 1988 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034 Connes, Alain; Shlyakhtenko, Dimitri 30 2005 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006 Connes, Alain; Consani, Caterina 30 2011 Classification des facteurs. Zbl 0503.46043 Connes, A. 28 1982 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013 Connes, Alain; Moscovici, Henri 28 2001 Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067 Connes, A.; Cuntz, J. 27 1988 Fun with \(\mathbb F_1\). Zbl 1228.11143 Connes, Alain; Consani, Caterina; Marcolli, Matilde 27 2009 KMS states and complex multiplication. Zbl 1106.58005 Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 27 2005 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001 Connes, Alain; Consani, Caterina; Marcolli, Matilde 26 2007 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190 Chamseddine, Ali H.; Connes, Alain 26 2007 Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069 Connes, A.; Gromov, M.; Moscovici, H. 26 1993 Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Zbl 0840.57013 Connes, Alain; Sullivan, Dennis; Teleman, Nicolas 26 1994 The arithmetic site. (Le site arithmétique.) Zbl 1315.11054 Connes, Alain; Consani, Caterina 26 2014 Scale invariance in the spectral action. Zbl 1112.83036 Chamseddine, Ali H.; Connes, Alain 25 2006 A walk in the noncommutative garden. Zbl 1145.14005 Connes, Alain; Marcolli, Matilde 25 2008 Characteristic 1, entropy and the absolute point. Zbl 1273.11140 Connes, Alain; Consani, Caterina 25 2011 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006 Connes, Alain; Moscovici, Henri 25 2000 Approximately transitive flows and ITPFI factors. Zbl 0606.46041 Connes, A.; Woods, E. J. 25 1985 Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006 Connes, Alain; Moscovici, Henri 25 1993 Spectral triples and \(\zeta\)-cycles. Zbl 07724321 Connes, Alain; Consani, Caterina 4 2023 Tolerance relations and operator systems. Zbl 07614112 Connes, Alain; van Suijlekom, Walter D. 3 2022 Spectral truncations in noncommutative geometry and operator systems. Zbl 1475.46062 Connes, Alain; van Suijlekom, Walter Daniël 22 2021 On absolute algebraic geometry the affine case. Zbl 1478.14047 Connes, Alain; Consani, Caterina 7 2021 Noncommutative geometry, the spectral standpoint. Zbl 1524.58003 Connes, Alain 4 2021 Weil positivity and trace formula the Archimedean place. Zbl 1480.46084 Connes, Alain; Consani, Caterina 4 2021 Segal’s gamma rings and universal arithmetic. Zbl 1484.14003 Connes, Alain; Consani, Caterina 4 2021 Memories of Vaughan Jones. Zbl 1480.01028 Bisch, Dietmar; Evans, David E.; Kirby, Robion; Popa, Sorin 3 2021 Quasi-inner functions and local factors. Zbl 1476.46071 Connes, Alain; Consani, Caterina 2 2021 The scaling Hamiltonian. Zbl 1524.11171 Connes, Alain; Consani, Caterina 1 2021 Entropy and the spectral action. Zbl 1444.46049 Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 12 2020 \(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061 Connes, Alain; Consani, Caterina 6 2020 The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008 Connes, Alain; Fathizadeh, Farzad 13 2019 Homological algebra in characteristic one. Zbl 1411.18006 Connes, Alain; Consani, Caterina 11 2019 Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032 Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D. 8 2019 The Riemann-Roch strategy. Complex lift of the scaling site. Zbl 1458.11108 Connes, Alain; Consani, Caterina 3 2019 Noncommutative geometry for symmetric non-self-adjoint operators. Zbl 07063161 Connes, Alain; Levitina, Galina; McDonald, Edward; Sukochev, Fedor; Zanin, Dmitriy 2 2019 Sir Michael Atiyah, a knight mathematician: a tribute to Michael Atiyah, an inspiration and a friend. Zbl 1427.01016 Connes, Alain; Kouneiher, Joseph 1 2019 Ronald G. Douglas: a master in the art of transcending problems. Zbl 1427.01030 Yu, Guoliang; Howe, Roger; Hutchins, Shana 1 2019 Geometry and the quantum. Zbl 1411.58003 Connes, Alain 4 2018 Geometry of the scaling site. Zbl 1406.11118 Connes, Alain; Consani, Caterina 10 2017 Trace theorem for quasi-Fuchsian groups. Zbl 1455.30035 Connes, Alain; Sukochev, Fedor A.; Zanin, Dmitriy V. 7 2017 Geometry of the arithmetic site. Zbl 1368.14038 Connes, Alain; Consani, Caterina 23 2016 Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046 Connes, Alain; Consani, Caterina 14 2016 An essay on the Riemann hypothesis. Zbl 1353.11095 Connes, Alain 8 2016 The scaling site. (Le site des fréquences.) Zbl 1348.18004 Connes, Alain; Consani, Caterina 6 2016 Grand unification in the spectral Pati-Salam model. Zbl 1388.81965 Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 20 2015 Universal thickening of the field of real numbers. Zbl 1387.11086 Connes, Alain; Consani, Caterina 14 2015 Cyclic structures and the topos of simplicial sets. Zbl 1328.19005 Connes, Alain; Consani, Caterina 9 2015 Projective geometry in characteristic one and the epicyclic category. Zbl 1338.19004 Connes, Alain; Consani, Caterina 7 2015 The cyclic and epicyclic sites. Zbl 1331.18005 Connes, Alain; Consani, Caterina 2 2015 Modular curvature for noncommutative two-tori. Zbl 1332.46070 Connes, Alain; Moscovici, Henri 59 2014 The arithmetic site. (Le site arithmétique.) Zbl 1315.11054 Connes, Alain; Consani, Caterina 26 2014 Geometry and the quantum: basics. Zbl 1333.81414 Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav 17 2014 On the arithmetic of the BC-system. Zbl 1302.11069 Connes, Alain; Consani, Caterina 9 2014 Cyclic homology, Serre’s local factors and \(\lambda\)-operations. Zbl 1327.14109 Connes, Alain; Consani, Caterina 6 2014 On the spectral characterization of manifolds. Zbl 1287.58004 Connes, Alain 98 2013 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032 Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 39 2013 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014 Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 33 2013 Resilience of the spectral standard model. Zbl 1397.81412 Chamseddine, Ali H.; Connes, Alain 34 2012 Spectral action for Robertson-Walker metrics. Zbl 1397.81413 Chamseddine, Ali H.; Connes, Alain 15 2012 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037 Connes, Alain; Tretkoff, Paula 54 2011 The hyperring of adèle classes. Zbl 1221.14002 Connes, Alain; Consani, Caterina 43 2011 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006 Connes, Alain; Consani, Caterina 30 2011 Characteristic 1, entropy and the absolute point. Zbl 1273.11140 Connes, Alain; Consani, Caterina 25 2011 The Witt construction in characteristic one and quantization. Zbl 1245.13015 Connes, Alain 10 2011 Noncommutative geometric spaces with boundary: spectral action. Zbl 1209.53061 Chamseddine, Ali H.; Connes, Alain 2 2011 Noncommutative geometry and global analysis. Conference in honor of Henri Moscovici, Bonn, Germany, June 29–July 4, 2009. Zbl 1218.00012 1 2011 Noncommutative geometry. Abstracts from the workshop held September 11–17, 2011. Zbl 1349.00115 1 2011 The BC-system and \(L\)-functions. Zbl 1276.14002 Connes, Alain 1 2011 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001 Connes, Alain; Consani, Caterina 62 2010 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130 Chamseddine, Ali H.; Connes, Alain 35 2010 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002 Connes, Alain; Consani, Caterina 31 2010 The uncanny precision of the spectral action. Zbl 1192.58005 Chamseddine, Ali H.; Connes, Alain 23 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 1185.00038 1 2010 Fun with \(\mathbb F_1\). Zbl 1228.11143 Connes, Alain; Consani, Caterina; Marcolli, Matilde 27 2009 The Weil proof and the geometry of the adelès class space. Zbl 1208.11108 Connes, Alain; Consani, Caterina; Marcolli, Matilde 14 2009 Renormalization and Galois theories. Selected papers of the CIRM workshop, Luminy, France, March 2006. Zbl 1173.14003 1 2009 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007 Connes, Alain; Marcolli, Matilde 128 2008 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004 Connes, Alain; Marcolli, Matilde 83 2008 Why the standard model. Zbl 1140.81021 Chamseddine, Ali H.; Connes, Alain 59 2008 Type III and spectral triples. Zbl 1159.46041 Connes, Alain; Moscovici, Henri 57 2008 A walk in the noncommutative garden. Zbl 1145.14005 Connes, Alain; Marcolli, Matilde 25 2008 Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres. Zbl 1159.58003 Connes, Alain; Dubois-Violette, Michel 10 2008 A unitary invariant in Riemannian geometry. Zbl 1197.46030 Connes, Alain 5 2008 Gravity and the standard model with neutrino mixing. Zbl 1140.81022 Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 149 2007 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001 Connes, Alain; Consani, Caterina; Marcolli, Matilde 26 2007 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190 Chamseddine, Ali H.; Connes, Alain 26 2007 Quantum gravity boundary terms from the spectral action of noncommutative space. Zbl 1228.83080 Chamseddine, Ali H.; Connes, Alain 20 2007 Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory. Zbl 1200.81113 Connes, Alain; Marcolli, Matilde 16 2007 Yang-Mills and some related algebras. Zbl 1177.58009 Connes, Alain; Dubois-Violette, Michel 10 2007 A property of parallelograms inscribed in ellipses. Zbl 1140.51010 Connes, Alain; Zagier, Don 9 2007 Noncommutative geometry. Abstracts from the workshop held September 2–8, 2007. Zbl 1177.58003 2 2007 On the foundations of noncommutative geometry. Zbl 1106.58004 Connes, A. 222 2006 Scale invariance in the spectral action. Zbl 1112.83036 Chamseddine, Ali H.; Connes, Alain 25 2006 From physics to number theory via noncommutative geometry. 2nd printing. Zbl 1126.58006 Connes, Alain; Marcolli, Matilde 21 2006 Inner fluctuations of the spectral action. Zbl 1105.58004 Connes, Alain; Chamseddine, Ali H. 20 2006 Quantum fields and motives. Zbl 1092.81050 Connes, Alain; Marcolli, Matilde 13 2006 KMS states and complex multiplication. II. Zbl 1123.58004 Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 9 2006 Noncommutative geometry and physics. Zbl 1129.83012 Connes, Alain 8 2006 \(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. Zbl 1139.58003 Connes, Alain; Marcolli, Matilde 4 2006 Morse inequalities for foliations. Zbl 1112.57007 Connes, Alain; Fack, Thierry 1 2006 Transgressions of the Godbillon-Vey class and Rademacher functions. Zbl 1109.11027 Connes, Alain; Moscovici, Henri 1 2006 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034 Connes, Alain; Shlyakhtenko, Dimitri 30 2005 KMS states and complex multiplication. Zbl 1106.58005 Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 27 2005 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012 Connes, Alain 46 2004 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024 Connes, Alain; Moscovici, Henri 36 2004 Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023 Connes, Alain; Moscovici, Henri 21 2004 Renormalization and motivic Galois theory. Zbl 1131.81021 Connes, Alain; Marcolli, Matilde 9 2004 Cyclic cohomology, noncommutative geometry and quantum group symmetries. Zbl 1052.46057 Connes, Alain 7 2004 Renormalization and Galois ambiguity. (Renormalisation et ambiguïté galoisienne.) Zbl 1072.81045 Connes, Alain 1 2004 Moduli space and structure of noncommutative 3-spheres. Zbl 1052.58012 Connes, Alain; Dubois-Violette, Michel 17 2003 Galois symmetries and renormalization. (Symétries galoisiennes et renormalisation.) Zbl 1050.81052 Connes, Alain 1 2003 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005 Connes, Alain; Dubois-Violette, Michel 102 2002 Yang-Mills algebra. Zbl 1028.53025 Connes, Alain; Dubois-Violette, Michel 31 2002 Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Zbl 1033.81061 Connes, A.; Kreimer, D. 18 2002 Noncommutative geometry year 2000. Zbl 1138.58304 Connes, Alain 6 2002 Hommage à Laurent Schwartz. Zbl 1015.01013 Connes, Alain 1 2002 Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045 Connes, Alain; Landi, Giovanni 121 2001 Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059 Connes, Alain; Kreimer, Dirk 119 2001 ...and 141 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,011 Authors 93 Connes, Alain 66 Guo, Li 61 Sukochev, Fedor Anatol’evich 56 Marcolli, Matilde 48 Popa, Sorin Teodor 46 van Suijlekom, Walter Daniël 41 Majid, Shahn 38 Landi, Giovanni 35 Sitarz, Andrzej 34 Khalkhali, Masoud 33 Rennie, Adam 33 Vaes, Stefaan 32 Dabrowski, Ludwik 31 Wang, Yong 30 Houdayer, Cyril 30 Iochum, Bruno 30 Longo, Roberto 30 Yu, Guoliang 29 Carey, Alan L. 29 Gao, Xing 29 Zanin, Dmitriy V. 28 Martinetti, Pierre 27 Consani, Caterina 27 Ioana, Adrian 27 Ponge, Raphaël S. 26 Lizzi, Fedele 25 Benameur, Moulay-Tahar 25 Ebrahimi-Fard, Kurusch 25 Neshveyev, Sergey V. 24 Chamseddine, Ali Hani 24 Jørgensen, Palle E. T. 24 Mathai, Varghese 23 Cho, Ilwoo 23 Haagerup, Uffe Valentin 23 Kaad, Jens 23 Laca, Marcelo 23 Skandalis, Georges 22 Wulkenhaar, Raimar 21 D’Andrea, Francesco 21 Golodets, Valentin Yakovlevich 21 Goswami, Debashish 21 Latrémolière, Frédéric 21 Nest, Ryszard 21 Wallet, Jean-Christophe 20 Bai, Chengming 20 Foissy, Loïc 20 Lorscheid, Oliver 19 Dubois-Violette, Michel 19 Narnhofer, Heide 19 Schücker, Thomas 18 Brzeziński, Tomasz 18 Chifan, Ionuţ 18 Junge, Marius 18 Manchon, Dominique 18 Xia, Jingbo 17 Moscovici, Henri 17 Paycha, Sylvie 17 Rangipour, Bahram 17 Savin, Anton Yur’evich 17 Sheng, Yunhe 17 Størmer, Erling 16 Chakraborty, Partha Sarathi 16 Elliott, George A. 16 Jun, Jaiung 16 Voiculescu, Dan-Virgil 15 Bhowmick, Jyotishman 15 Choda, Marie 15 Dadarlat, Marius 15 Fidaleo, Francesco 15 Klimek, Slawomir 15 Nistor, Victor 15 Patras, Frédéric 15 Schulz-Baldes, Hermann 15 Shlyakhtenko, Dimitri L. 15 Takesaki, Masamichi 14 Aastrup, Johannes 14 Castro Perelman, Carlos 14 Cuntz, Joachim 14 Fathizadeh, Farzad 14 Gracia-Bondía, José M. 14 Grosse, Harald 14 Jones, Vaughan Frederick Randal 14 Meyer, Ralf 14 Schrohe, Elmar 14 Sims, Aidan 14 Stephan, Christoph A. 13 Christensen, Erik 13 Goffeng, Magnus 13 Guin, Satyajit 13 Hochs, Peter 13 Isono, Yusuke 13 Lesniewski, Andrzej 13 Marrakchi, Amine 13 Mesland, Bram 13 Tang, Xiang 13 Tomatsu, Reiji 13 Usachev, Aleksandr Sergeevich 13 Várilly, Joseph C. 13 Wang, Hang 13 Wang, Jian ...and 3,911 more Authors all top 5 Cited in 431 Serials 418 Journal of Functional Analysis 347 Communications in Mathematical Physics 253 Journal of Geometry and Physics 212 Advances in Mathematics 210 Journal of Mathematical Physics 192 Journal of Noncommutative Geometry 161 Letters in Mathematical Physics 118 Proceedings of the American Mathematical Society 117 Journal of High Energy Physics 105 Transactions of the American Mathematical Society 92 Nuclear Physics. B 83 Journal of Algebra 75 \(K\)-Theory 73 Journal of Pure and Applied Algebra 71 Mathematische Annalen 64 Ergodic Theory and Dynamical Systems 62 International Journal of Mathematics 60 Publications of the Research Institute for Mathematical Sciences, Kyoto University 58 Inventiones Mathematicae 58 International Journal of Geometric Methods in Modern Physics 56 Journal of Mathematical Analysis and Applications 54 Comptes Rendus. Mathématique. Académie des Sciences, Paris 52 Reviews in Mathematical Physics 49 International Journal of Modern Physics A 49 International Journal of Theoretical Physics 44 Physics Letters. B 44 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 42 Israel Journal of Mathematics 42 Chaos, Solitons and Fractals 41 Journal für die Reine und Angewandte Mathematik 40 Journal of Physics A: Mathematical and Theoretical 34 Communications in Algebra 32 Annales de l’Institut Fourier 32 Bulletin of the American Mathematical Society. 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Studies in History and Philosophy of Modern Physics 11 Forum of Mathematics, Sigma 10 Manuscripta Mathematica 10 Nuclear Physics. B. Proceedings Supplements ...and 331 more Serials all top 5 Cited in 62 Fields 2,596 Functional analysis (46-XX) 1,513 Quantum theory (81-XX) 1,151 Global analysis, analysis on manifolds (58-XX) 699 Associative rings and algebras (16-XX) 552 \(K\)-theory (19-XX) 518 Operator theory (47-XX) 468 Topological groups, Lie groups (22-XX) 463 Differential geometry (53-XX) 440 Nonassociative rings and algebras (17-XX) 400 Relativity and gravitational theory (83-XX) 388 Dynamical systems and ergodic theory (37-XX) 345 Group theory and generalizations (20-XX) 324 Category theory; homological algebra (18-XX) 282 Number theory (11-XX) 252 Algebraic geometry (14-XX) 226 Manifolds and cell complexes (57-XX) 212 Combinatorics (05-XX) 200 Algebraic topology (55-XX) 186 Measure and integration (28-XX) 177 Statistical mechanics, structure of matter (82-XX) 145 Abstract harmonic analysis (43-XX) 135 Partial differential equations (35-XX) 127 Probability theory and stochastic processes (60-XX) 85 Mathematical logic and foundations (03-XX) 78 Commutative algebra (13-XX) 75 Several complex variables and analytic spaces (32-XX) 71 Linear and multilinear algebra; matrix theory (15-XX) 60 Order, lattices, ordered algebraic structures (06-XX) 60 General topology (54-XX) 55 Information and communication theory, circuits (94-XX) 50 Field theory and polynomials (12-XX) 46 Ordinary differential equations (34-XX) 46 Geometry (51-XX) 45 Mechanics of particles and systems (70-XX) 44 Harmonic analysis on Euclidean spaces (42-XX) 41 Functions of a complex variable (30-XX) 40 Computer science (68-XX) 39 General and overarching topics; collections (00-XX) 38 Convex and discrete geometry (52-XX) 25 Numerical analysis (65-XX) 23 General algebraic systems (08-XX) 23 Special functions (33-XX) 22 History and biography (01-XX) 18 Statistics (62-XX) 15 Real functions (26-XX) 15 Classical thermodynamics, heat transfer (80-XX) 13 Difference and functional equations (39-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Optics, electromagnetic theory (78-XX) 12 Operations research, mathematical programming (90-XX) 10 Sequences, series, summability (40-XX) 10 Approximations and expansions (41-XX) 9 Potential theory (31-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Astronomy and astrophysics (85-XX) 6 Systems theory; control (93-XX) 5 Integral transforms, operational calculus (44-XX) 5 Integral equations (45-XX) 3 Fluid mechanics (76-XX) 3 Biology and other natural sciences (92-XX) 2 Mathematics education (97-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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