Edit Profile (opens in new tab) Connes, Alain Co-Author Distance Author ID: connes.alain Published as: Connes, Alain; Connes, A. Further Spellings: Конн Ален Homepage: http://www.alainconnes.org/en/ 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: 267 Publications since 1969, including 12 Books 21 Contributions as Editor · 5 Further Contributions Biographic References: 7 Publications Co-Authors: 88 Co-Authors with 182 Joint Publications 3,136 Co-Co-Authors all top 5 Co-Authors 109 single-authored 34 Consani, Caterina 22 Moscovici, Henri 18 Chamseddine, Ali Hani 14 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 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 Evans, David E. 2 Haagerup, Uffe Valentin 2 Higson, Nigel 2 Lichnerowicz, Andre 2 Lott, John 2 McDonald, Edward Andrew 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 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 Gawȩdzki, Krzysztof 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 Jaffe, Arthur Michael 1 Joseph, Anthony 1 Kaminker, Jerome 1 Kawahigashi, Yasuyuki 1 Khalkhali, Masoud 1 Kirby, Robion Cromwell 1 Kouneiher, Joseph 1 Krieger, Wolfgang 1 Lafforgue, Laurent 1 Landi, Giovanni 1 Lebowitz, Joel Louis 1 Lehrer, Gustav Isaac 1 Lesch, Matthias 1 Levitina, Galina Borisovna 1 Lewis, Albert C. 1 Longo, Roberto ...and 43 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 5 Journal of Number Theory 5 Notices of the American Mathematical Society 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 Higher Structures 1 Les Grandes Voix de la Recherche all top 5 Fields 157 Functional analysis (46-XX) 118 Global analysis, analysis on manifolds (58-XX) 73 Quantum theory (81-XX) 54 Number theory (11-XX) 37 \(K\)-theory (19-XX) 35 Algebraic geometry (14-XX) 34 General and overarching topics; collections (00-XX) 30 Associative rings and algebras (16-XX) 24 Manifolds and cell complexes (57-XX) 21 Category theory; homological algebra (18-XX) 15 Algebraic topology (55-XX) 14 Topological groups, Lie groups (22-XX) 13 History and biography (01-XX) 12 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 Field theory and polynomials (12-XX) 7 Group theory and generalizations (20-XX) 7 Operator theory (47-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Commutative algebra (13-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 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 Open 239 Publications have been cited 10,280 times in 5,375 Documents Cited by ▼ Year ▼ Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076Connes, Alain 690 1994 Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042Connes, Alain 394 1976 Non-commutative differential geometry. Zbl 0592.46056Connes, Alain 338 1985 Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004Connes, A. 308 1987 Une classification des facteurs de type III. Zbl 0274.46050Connes, Alain 283 1973 Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038Connes, Alain; Kreimer, Dirk 258 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 257 2000 Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009Connes, Alain 255 1996 On the foundations of noncommutative geometry. Zbl 1106.58004Connes, A. 220 2006 The local index formula in noncommutative geometry. Zbl 0960.46048Connes, A.; Moscovici, H. 208 1995 The spectral action principle. Zbl 0894.58007Chamseddine, Ali H.; Connes, Alain 208 1997 An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018Connes, A.; Feldman, J.; Weiss, B. 199 1981 Noncommutative geometry and reality. Zbl 0871.58008Connes, Alain 175 1995 Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061Baum, Paul; Connes, Alain; Higson, Nigel 146 1994 The longitudinal index theorem for foliations. Zbl 0575.58030Connes, A.; Skandalis, G. 145 1984 Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047Connes, Alain; Moscovici, Henri 142 1990 Gravity and the standard model with neutrino mixing. Zbl 1140.81022Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 140 2007 An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043Connes, A. 130 1981 Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005Connes, A.; Moscovici, H. 127 1998 Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040Bost, J.-B.; Connes, A. 124 1995 Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051Connes, A. 122 1989 The action functional in non-commutative geometry. Zbl 0658.53068Connes, A. 120 1988 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007Connes, Alain; Marcolli, Matilde 119 2008 Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045Connes, Alain; Landi, Giovanni 119 2001 Non-commutative geometry and physics. Zbl 0933.46069Connes, A. 119 1995 Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052Connes, Alain 116 1975 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 115 2001 The flow of weights on factors of type III. Zbl 0408.46047Connes, Alain; Takesaki, Masamichi 110 1977 Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009Connes, Alain 109 1983 C* algèbres et géométrie différentielle. Zbl 0433.46057Connes, Alain 107 1980 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015Connes, Alain 105 1999 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005Connes, Alain; Dubois-Violette, Michel 101 2002 Property \(T\) for von Neumann algebras. Zbl 1190.46047Connes, A.; Jones, V. 99 1985 Almost periodic states and factors of type III\(_1\). Zbl 0302.46050Connes, A. 98 1974 Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073Connes, A.; Narnhofer, H.; Thirring, W. 96 1987 Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052Connes, Alain; Douglas, Michael R.; Schwarz, Albert 95 1998 On the spectral characterization of manifolds. Zbl 1287.58004Connes, Alain 89 2013 A survey of foliations and operator algebras. Zbl 0531.57023Connes, A. 85 1982 Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032Connes, Alain; Størmer, Erling 83 1975 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 80 2008 On the spatial theory of von Neumann algebras. Zbl 0443.46042Connes, A. 79 1980 Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086Connes, A.; Rovelli, C. 74 1994 Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505Chamseddine, Ali H.; Connes, Alain 72 1996 Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078Connes, Alain 70 1974 Deformations, asymptotic morphisms and bivariant \(K\)-theory. (Déformations, morphismes asymptotiques et \(K\)-théorie bivariante.) Zbl 0717.46062Connes, Alain; Higson, Nigel 69 1990 Particle models and noncommutative geometry. Zbl 0957.46516Connes, Alain; Lott, John 67 1990 Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049Connes, A. 66 1988 Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027Connes, A. 61 1977 Modular curvature for noncommutative two-tori. Zbl 1332.46070Connes, Alain; Moscovici, Henri 58 2014 Property T and asymptotically invariant sequences. Zbl 0479.28017Connes, A.; Weiss, B. 57 1980 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 57 2008 Geometry from the spectral point of view. Zbl 1042.46515Connes, Alain 56 1995 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 56 2010 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 54 2008 Sur la théorie non commutative de l’intégration. Zbl 0412.46053Connes, Alain 52 1979 A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056Connes, A. 52 1980 On the cohomology of operator algebras. Zbl 0408.46042Connes, A. 51 1978 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 51 2011 Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048Connes, Alain; Størmer, Erling 49 1978 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 46 2004 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042Baum, Paul; Connes, Alain 45 2000 The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031Connes, Alain; Moscovici, Henri 44 1982 Introduction to non commutative differential geometry. Zbl 0564.58002Connes, A. 43 1985 Yang-Mills for non-commutative two-tori. Zbl 0633.46069Connes, Alain; Rieffel, Marc A. 41 1987 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 41 2011 Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054Connes, A. 39 1986 A factor not anti-isomorphic to itself. Zbl 0315.46058Connes, A. 39 1975 Cyclic cohomology and Hopf algebras. Zbl 0941.16024Connes, Alain; Moscovici, Henri 39 1999 A short survey of noncommutative geometry. Zbl 0974.58008Connes, Alain 38 2000 Closed star products and cyclic cohomology. Zbl 0767.55005Connes, Alain; Flato, Moshé; Sternheimer, Daniel 38 1992 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 37 2013 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 33 2004 Noncommutative geometry. (Géométrie non commutative.) Zbl 0745.46067Connes, Alain 33 1990 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 33 2012 A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056Connes, A.; Jones, V. 32 1982 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 32 2013 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 32 2010 Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013Connes, Alain; Krieger, Wolfgang 31 1977 Yang-Mills algebra. Zbl 1028.53025Connes, Alain; Dubois-Violette, Michel 30 2002 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 29 2010 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034Connes, Alain; Shlyakhtenko, Dimitri 28 2005 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 28 2001 Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067Connes, A.; Cuntz, J. 27 1988 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 27 2011 Chern character for discrete groups. Zbl 0656.55005Baum, Paul; Connes, Alain 26 1988 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 26 2007 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 25 2008 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006Connes, Alain; Moscovici, Henri 25 2000 Quantized calculus and applications. Zbl 1052.46510Connes, Alain 25 1995 KMS states and complex multiplication. Zbl 1106.58005Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 25 2005 Scale invariance in the spectral action. Zbl 1112.83036Chamseddine, Ali H.; Connes, Alain 25 2006 Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069Connes, A.; Gromov, M.; Moscovici, H. 25 1993 Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006Connes, Alain; Moscovici, Henri 25 1993 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 25 2007 Approximately transitive flows and ITPFI factors. Zbl 0606.46041Connes, A.; Woods, E. J. 24 1985 Fun with \(\mathbb F_1\). Zbl 1228.11143Connes, Alain; Consani, Caterina; Marcolli, Matilde 24 2009 Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Zbl 0840.57013Connes, Alain; Sullivan, Dennis; Teleman, Nicolas 24 1994 Factors of type \(III_ 1\), property \(L_{\lambda}'\) and closure of inner automorphisms. Zbl 0597.46063Connes, A. 23 1985 The arithmetic site. (Le site arithmétique.) Zbl 1315.11054Connes, Alain; Consani, Caterina 23 2014 Characteristic 1, entropy and the absolute point. Zbl 1273.11140Connes, Alain; Consani, Caterina 23 2011 Spectral triples and \(\zeta\)-cycles. Zbl 07724321Connes, Alain; Consani, Caterina 2 2023 Tolerance relations and operator systems. Zbl 07614112Connes, Alain; van Suijlekom, Walter D. 2 2022 Spectral truncations in noncommutative geometry and operator systems. Zbl 1475.46062Connes, Alain; van Suijlekom, Walter Daniël 16 2021 On absolute algebraic geometry the affine case. Zbl 1478.14047Connes, Alain; Consani, Caterina 5 2021 Noncommutative geometry, the spectral standpoint. Zbl 07425826Connes, Alain 3 2021 Segal’s gamma rings and universal arithmetic. Zbl 1484.14003Connes, Alain; Consani, Caterina 2 2021 Quasi-inner functions and local factors. Zbl 1476.46071Connes, Alain; Consani, Caterina 1 2021 Weil positivity and trace formula the Archimedean place. Zbl 1480.46084Connes, Alain; Consani, Caterina 1 2021 Entropy and the spectral action. Zbl 1444.46049Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 8 2020 \(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061Connes, Alain; Consani, Caterina 5 2020 The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008Connes, Alain; Fathizadeh, Farzad 13 2019 Homological algebra in characteristic one. Zbl 1411.18006Connes, Alain; Consani, Caterina 9 2019 Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D. 8 2019 The Riemann-Roch strategy. Complex lift of the scaling site. Zbl 1458.11108Connes, Alain; Consani, Caterina 2 2019 Noncommutative geometry for symmetric non-self-adjoint operators. Zbl 07063161Connes, 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 1427.01016Connes, Alain; Kouneiher, Joseph 1 2019 Ronald G. Douglas: a master in the art of transcending problems. Zbl 1427.01030Yu, Guoliang; Howe, Roger; Hutchins, Shana 1 2019 Geometry and the quantum. Zbl 1411.58003Connes, Alain 3 2018 Geometry of the scaling site. Zbl 1406.11118Connes, Alain; Consani, Caterina 8 2017 Trace theorem for quasi-Fuchsian groups. Zbl 1455.30035Connes, Alain; Sukochev, Fedor A.; Zanin, Dmitriy V. 6 2017 Geometry of the arithmetic site. Zbl 1368.14038Connes, Alain; Consani, Caterina 21 2016 Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046Connes, Alain; Consani, Caterina 12 2016 An essay on the Riemann hypothesis. Zbl 1353.11095Connes, Alain 7 2016 The scaling site. (Le site des fréquences.) Zbl 1348.18004Connes, Alain; Consani, Caterina 6 2016 Grand unification in the spectral Pati-Salam model. Zbl 1388.81965Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 19 2015 Universal thickening of the field of real numbers. Zbl 1387.11086Connes, Alain; Consani, Caterina 14 2015 Cyclic structures and the topos of simplicial sets. Zbl 1328.19005Connes, Alain; Consani, Caterina 9 2015 Projective geometry in characteristic one and the epicyclic category. Zbl 1338.19004Connes, Alain; Consani, Caterina 7 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 58 2014 The arithmetic site. (Le site arithmétique.) Zbl 1315.11054Connes, Alain; Consani, Caterina 23 2014 Geometry and the quantum: basics. Zbl 1333.81414Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav 16 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 89 2013 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 37 2013 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 32 2013 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 33 2012 Spectral action for Robertson-Walker metrics. Zbl 1397.81413Chamseddine, Ali H.; Connes, Alain 15 2012 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 51 2011 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 41 2011 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 27 2011 Characteristic 1, entropy and the absolute point. Zbl 1273.11140Connes, Alain; Consani, Caterina 23 2011 The Witt construction in characteristic one and quantization. Zbl 1245.13015Connes, Alain 9 2011 Noncommutative geometric spaces with boundary: spectral action. Zbl 1209.53061Chamseddine, Ali H.; Connes, Alain 2 2011 Noncommutative geometry. Abstracts from the workshop held September 11–17, 2011. Zbl 1349.00115 1 2011 The BC-system and \(L\)-functions. Zbl 1276.14002Connes, Alain 1 2011 Noncommutative geometry and global analysis. Conference in honor of Henri Moscovici, Bonn, Germany, June 29–July 4, 2009. Zbl 1218.00012 1 2011 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 56 2010 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 32 2010 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 29 2010 The uncanny precision of the spectral action. Zbl 1192.58005Chamseddine, Ali H.; Connes, Alain 21 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 1228.11143Connes, Alain; Consani, Caterina; Marcolli, Matilde 24 2009 The Weil proof and the geometry of the adelès class space. Zbl 1208.11108Connes, 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 1209.58007Connes, Alain; Marcolli, Matilde 119 2008 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 80 2008 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 57 2008 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 54 2008 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 25 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 140 2007 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 26 2007 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 25 2007 Quantum gravity boundary terms from the spectral action of noncommutative space. Zbl 1228.83080Chamseddine, Ali H.; Connes, Alain 19 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 7 2007 Noncommutative geometry. Abstracts from the workshop held September 2–8, 2007. Zbl 1177.58003 2 2007 On the foundations of noncommutative geometry. Zbl 1106.58004Connes, A. 220 2006 Scale invariance in the spectral action. Zbl 1112.83036Chamseddine, Ali H.; Connes, Alain 25 2006 Inner fluctuations of the spectral action. Zbl 1105.58004Connes, Alain; Chamseddine, Ali H. 20 2006 From physics to number theory via noncommutative geometry. 2nd printing. Zbl 1126.58006Connes, Alain; Marcolli, Matilde 20 2006 Quantum fields and motives. Zbl 1092.81050Connes, Alain; Marcolli, Matilde 13 2006 KMS states and complex multiplication. II. Zbl 1123.58004Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 9 2006 Noncommutative geometry and physics. Zbl 1129.83012Connes, Alain 8 2006 \(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. Zbl 1139.58003Connes, Alain; Marcolli, Matilde 4 2006 Transgressions of the Godbillon-Vey class and Rademacher functions. Zbl 1109.11027Connes, Alain; Moscovici, Henri 1 2006 Morse inequalities for foliations. Zbl 1112.57007Connes, Alain; Fack, Thierry 1 2006 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034Connes, Alain; Shlyakhtenko, Dimitri 28 2005 KMS states and complex multiplication. Zbl 1106.58005Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 25 2005 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 46 2004 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 33 2004 Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023Connes, Alain; Moscovici, Henri 21 2004 Renormalization and motivic Galois theory. Zbl 1131.81021Connes, Alain; Marcolli, Matilde 9 2004 Cyclic cohomology, noncommutative geometry and quantum group symmetries. Zbl 1052.46057Connes, Alain 7 2004 Renormalization and Galois ambiguity. (Renormalisation et ambiguïté galoisienne.) Zbl 1072.81045Connes, Alain 1 2004 Moduli space and structure of noncommutative 3-spheres. Zbl 1052.58012Connes, Alain; Dubois-Violette, Michel 17 2003 Galois symmetries and renormalization. (Symétries galoisiennes et renormalisation.) Zbl 1050.81052Connes, Alain 1 2003 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005Connes, Alain; Dubois-Violette, Michel 101 2002 Yang-Mills algebra. Zbl 1028.53025Connes, Alain; Dubois-Violette, Michel 30 2002 Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Zbl 1033.81061Connes, A.; Kreimer, D. 17 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 119 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 115 2001 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 28 2001 From local perturbation theory to Hopf- and Lie-algebras of Feynman graphs. Zbl 1015.81042Connes, A.; Kreimer, D. 4 2001 ...and 139 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,783 Authors 91 Connes, Alain 59 Sukochev, Fedor Anatol’evich 58 Guo, Li 54 Marcolli, Matilde 47 Popa, Sorin Teodor 42 van Suijlekom, Walter Daniël 36 Landi, Giovanni 35 Majid, Shahn 34 Sitarz, Andrzej 33 Rennie, Adam 32 Dabrowski, Ludwik 32 Khalkhali, Masoud 32 Vaes, Stefaan 30 Houdayer, Cyril 30 Iochum, Bruno 29 Carey, Alan L. 29 Longo, Roberto 27 Ponge, Raphaël S. 27 Yu, Guoliang 27 Zanin, Dmitriy V. 26 Consani, Caterina 26 Gao, Xing 26 Martinetti, Pierre 25 Ebrahimi-Fard, Kurusch 25 Lizzi, Fedele 24 Benameur, Moulay-Tahar 24 Chamseddine, Ali Hani 24 Ioana, Adrian 24 Neshveyev, Sergey V. 24 Wang, Yong 23 Haagerup, Uffe Valentin 23 Laca, Marcelo 23 Mathai, Varghese 23 Skandalis, Georges 22 Jørgensen, Palle E. T. 22 Kaad, Jens 21 D’Andrea, Francesco 21 Golodets, Valentin Yakovlevich 21 Goswami, Debashish 20 Cho, Ilwoo 20 Nest, Ryszard 19 Dubois-Violette, Michel 19 Foissy, Loïc 19 Latrémolière, Frédéric 19 Narnhofer, Heide 19 Schücker, Thomas 19 Wulkenhaar, Raimar 18 Bai, Chengming 18 Junge, Marius 18 Lorscheid, Oliver 18 Wallet, Jean-Christophe 17 Brzeziński, Tomasz 17 Chifan, Ionuţ 17 Moscovici, Henri 17 Rangipour, Bahram 17 Savin, Anton Yur’evich 17 Størmer, Erling 17 Thomsen, Klaus E. 16 Chakraborty, Partha Sarathi 16 Manchon, Dominique 16 Voiculescu, Dan-Virgil 16 Xia, Jingbo 15 Bhowmick, Jyotishman 15 Choda, Marie 15 Dadarlat, Marius 15 Elliott, George A. 15 Klimek, Slawomir 15 Nistor, Victor 15 Patras, Frédéric 15 Shlyakhtenko, Dimitri L. 15 Takesaki, Masamichi 14 Castro Perelman, Carlos 14 Cuntz, Joachim 14 Fathizadeh, Farzad 14 Fidaleo, Francesco 14 Gracia-Bondía, José M. 14 Jun, Jaiung 14 Paycha, Sylvie 14 Schrohe, Elmar 14 Schulz-Baldes, Hermann 14 Sheng, Yunhe 14 Sims, Aidan 14 Stephan, Christoph A. 13 Christensen, Erik 13 Goffeng, Magnus 13 Grosse, Harald 13 Hochs, Peter 13 Isono, Yusuke 13 Jones, Vaughan Frederick Randal 13 Lesniewski, Andrzej 13 Marrakchi, Amine 13 Meyer, Ralf 13 Tomatsu, Reiji 13 Usachev, Aleksandr Sergeevich 13 Várilly, Joseph C. 13 Winter, Wilhelm 12 Aastrup, Johannes 12 Bellissard, Jean V. 12 Gayral, Victor 12 Guin, Satyajit ...and 3,683 more Authors all top 5 Cited in 417 Serials 408 Journal of Functional Analysis 340 Communications in Mathematical Physics 247 Journal of Geometry and Physics 205 Advances in Mathematics 196 Journal of Mathematical Physics 178 Journal of Noncommutative Geometry 158 Letters in Mathematical Physics 117 Proceedings of the American Mathematical Society 104 Transactions of the American Mathematical Society 103 Journal of High Energy Physics 90 Nuclear Physics. 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Series A 12 Journal of the American Mathematical Society 12 Algebras and Representation Theory 12 Journal of the Australian Mathematical Society 11 Publications Mathématiques 11 Journal of Soviet Mathematics 11 Linear Algebra and its Applications 11 Journal of Homotopy and Related Structures 11 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 11 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 10 Studia Mathematica 10 Journal of the London Mathematical Society. Second Series 10 Manuscripta Mathematica 10 Nuclear Physics. B. Proceedings Supplements 10 Geometry & Topology 10 Annals of \(K\)-Theory 9 Differential Geometry and its Applications 9 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 9 Annales de l’Institut Henri Poincaré. Physique Théorique ...and 317 more Serials all top 5 Cited in 62 Fields 2,490 Functional analysis (46-XX) 1,426 Quantum theory (81-XX) 1,102 Global analysis, analysis on manifolds (58-XX) 664 Associative rings and algebras (16-XX) 538 \(K\)-theory (19-XX) 487 Operator theory (47-XX) 441 Topological groups, Lie groups (22-XX) 422 Differential geometry (53-XX) 413 Nonassociative rings and algebras (17-XX) 375 Relativity and gravitational theory (83-XX) 369 Dynamical systems and ergodic theory (37-XX) 327 Group theory and generalizations (20-XX) 308 Category theory; homological algebra (18-XX) 269 Number theory (11-XX) 229 Algebraic geometry (14-XX) 214 Manifolds and cell complexes (57-XX) 198 Combinatorics (05-XX) 186 Algebraic topology (55-XX) 183 Measure and integration (28-XX) 168 Statistical mechanics, structure of matter (82-XX) 140 Abstract harmonic analysis (43-XX) 124 Partial differential equations (35-XX) 115 Probability theory and stochastic processes (60-XX) 81 Mathematical logic and foundations (03-XX) 75 Commutative algebra (13-XX) 66 Linear and multilinear algebra; matrix theory (15-XX) 66 Several complex variables and analytic spaces (32-XX) 56 Order, lattices, ordered algebraic structures (06-XX) 56 General topology (54-XX) 48 Field theory and polynomials (12-XX) 48 Information and communication theory, circuits (94-XX) 43 Ordinary differential equations (34-XX) 40 Mechanics of particles and systems (70-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 38 Geometry (51-XX) 37 Functions of a complex variable (30-XX) 36 Computer science (68-XX) 35 General and overarching topics; collections (00-XX) 34 Convex and discrete geometry (52-XX) 21 History and biography (01-XX) 21 General algebraic systems (08-XX) 21 Special functions (33-XX) 21 Numerical analysis (65-XX) 13 Statistics (62-XX) 13 Classical thermodynamics, heat transfer (80-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Real functions (26-XX) 12 Difference and functional equations (39-XX) 11 Optics, electromagnetic theory (78-XX) 10 Sequences, series, summability (40-XX) 10 Operations research, mathematical programming (90-XX) 9 Approximations and expansions (41-XX) 9 Astronomy and astrophysics (85-XX) 8 Potential theory (31-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Systems theory; control (93-XX) 5 Integral transforms, operational calculus (44-XX) 5 Integral equations (45-XX) 4 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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