Edit Profile (opens in new tab) Connes, Alain Compute Distance To: Compute 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: 261 Publications since 1969, including 11 Books 19 Contributions as Editor · 5 Further Contributions Biographic References: 7 Publications Co-Authors: 79 Co-Authors with 175 Joint Publications 3,010 Co-Co-Authors all top 5 Co-Authors 108 single-authored 29 Consani, Caterina 21 Moscovici, Henri 18 Chamseddine, Ali Hani 14 Marcolli, Matilde 9 Kreimer, Dirk 7 Cuntz, Joachim 6 Baum, Paul Frank 6 Gromov, Mikhael Leonidovich 6 Rieffel, Marc A. 6 van Suijlekom, Walter Daniël 6 Yu, Guoliang 5 Dubois-Violette, Michel 4 Alon, Noga M. 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 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 Nest, Ryszard 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 Cheeger, Jeff 1 Coburn, Lewis A. 1 Conder, Marston D. E. 1 Damour, Thibault 1 de la Harpe, Pierre 1 Dehen, Michele 1 Donnelly, Harold 1 Duflo, Michel 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 Jaffe, Arthur Michael 1 Joseph, Anthony 1 Kaminker, Jerome 1 Kawahigashi, Yasuyuki 1 Kirby, Robion Cromwell 1 Kouneiher, Joseph 1 Krieger, Wolfgang 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 1 Louveau, Alain 1 Martin, Gaven J. 1 Misra, Gadadhar 1 Mokobodzki, Gabriel 1 Mukhanov, Viatcheslav F. 1 Musat, Magdalena 1 Narnhofer, Heide ...and 32 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 8 Journal of Geometry and Physics 8 Oberwolfach Reports 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 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 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 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 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 155 Functional analysis (46-XX) 115 Global analysis, analysis on manifolds (58-XX) 72 Quantum theory (81-XX) 51 Number theory (11-XX) 34 \(K\)-theory (19-XX) 32 Algebraic geometry (14-XX) 31 General and overarching topics; collections (00-XX) 29 Associative rings and algebras (16-XX) 24 Manifolds and cell complexes (57-XX) 19 Category theory; homological algebra (18-XX) 14 Topological groups, Lie groups (22-XX) 14 Algebraic topology (55-XX) 13 Differential geometry (53-XX) 11 History and biography (01-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 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 Open 233 Publications have been cited 9,663 times in 5,070 Documents Cited by ▼ Year ▼ Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076Connes, Alain 641 1994 Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042Connes, Alain 370 1976 Non-commutative differential geometry. Zbl 0592.46056Connes, Alain 322 1985 Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004Connes, A. 276 1987 Une classification des facteurs de type III. Zbl 0274.46050Connes, Alain 270 1973 Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009Connes, Alain 249 1996 Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038Connes, Alain; Kreimer, Dirk 242 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 232 2000 On the foundations of noncommutative geometry. Zbl 1106.58004Connes, A. 208 2006 The local index formula in noncommutative geometry. Zbl 0960.46048Connes, A.; Moscovici, H. 201 1995 An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018Connes, A.; Feldman, J.; Weiss, B. 193 1981 The spectral action principle. Zbl 0894.58007Chamseddine, Ali H.; Connes, Alain 192 1997 Noncommutative geometry and reality. Zbl 0871.58008Connes, Alain 168 1995 The longitudinal index theorem for foliations. Zbl 0575.58030Connes, A.; Skandalis, G. 142 1984 Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047Connes, Alain; Moscovici, Henri 136 1990 Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061Baum, Paul; Connes, Alain; Higson, Nigel 133 1994 Gravity and the standard model with neutrino mixing. Zbl 1140.81022Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 128 2007 Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005Connes, A.; Moscovici, H. 126 1998 An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043Connes, A. 125 1981 Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040Bost, J.-B.; Connes, A. 121 1995 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. 115 1995 The action functional in non-commutative geometry. Zbl 0658.53068Connes, A. 114 1988 Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051Connes, A. 113 1989 Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052Connes, Alain 113 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 110 2001 The flow of weights on factors of type III. Zbl 0408.46047Connes, Alain; Takesaki, Masamichi 107 1977 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007Connes, Alain; Marcolli, Matilde 105 2008 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015Connes, Alain 100 1999 Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009Connes, Alain 100 1983 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005Connes, Alain; Dubois-Violette, Michel 99 2002 C* algèbres et géométrie différentielle. Zbl 0433.46057Connes, Alain 98 1980 Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073Connes, A.; Narnhofer, H.; Thirring, W. 94 1987 Almost periodic states and factors of type III\(_1\). Zbl 0302.46050Connes, A. 94 1974 Property \(T\) for von Neumann algebras. Zbl 1190.46047Connes, A.; Jones, V. 90 1985 Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052Connes, Alain; Douglas, Michael R.; Schwarz, Albert 81 1998 On the spectral characterization of manifolds. Zbl 1287.58004Connes, Alain 81 2013 Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032Connes, Alain; Størmer, Erling 80 1975 On the spatial theory of von Neumann algebras. Zbl 0443.46042Connes, A. 78 1980 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 74 2008 A survey of foliations and operator algebras. Zbl 0531.57023Connes, A. 71 1982 Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086Connes, A.; Rovelli, C. 68 1994 Deformations, asymptotic morphisms and bivariant \(K\)-theory. (Déformations, morphismes asymptotiques et \(K\)-théorie bivariante.) Zbl 0717.46062Connes, Alain; Higson, Nigel 67 1990 Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078Connes, Alain 66 1974 Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505Chamseddine, Ali H.; Connes, Alain 64 1996 Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049Connes, A. 64 1988 Particle models and noncommutative geometry. Zbl 0957.46516Connes, Alain; Lott, John 61 1990 Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027Connes, A. 57 1977 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 55 2008 Modular curvature for noncommutative two-tori. Zbl 1332.46070Connes, Alain; Moscovici, Henri 55 2014 Property T and asymptotically invariant sequences. Zbl 0479.28017Connes, A.; Weiss, B. 55 1980 Geometry from the spectral point of view. Zbl 1042.46515Connes, Alain 54 1995 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 52 2010 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 51 2008 A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056Connes, A. 51 1980 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 49 2011 On the cohomology of operator algebras. Zbl 0408.46042Connes, A. 49 1978 Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048Connes, Alain; Størmer, Erling 48 1978 Sur la théorie non commutative de l’intégration. Zbl 0412.46053Connes, Alain 46 1979 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 45 2004 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042Baum, Paul; Connes, Alain 42 2000 Introduction to non commutative differential geometry. Zbl 0564.58002Connes, A. 42 1985 The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031Connes, Alain; Moscovici, Henri 42 1982 A factor not anti-isomorphic to itself. Zbl 0315.46058Connes, A. 39 1975 Closed star products and cyclic cohomology. Zbl 0767.55005Connes, Alain; Flato, Moshé; Sternheimer, Daniel 38 1992 A short survey of noncommutative geometry. Zbl 0974.58008Connes, Alain 38 2000 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 38 2011 Cyclic cohomology and Hopf algebras. Zbl 0941.16024Connes, Alain; Moscovici, Henri 37 1999 Yang-Mills for non-commutative two-tori. Zbl 0633.46069Connes, Alain; Rieffel, Marc A. 37 1987 Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054Connes, A. 34 1986 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 33 2004 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. 31 2013 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 29 2002 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 29 2010 Noncommutative geometry. (Géométrie non commutative.) Zbl 0745.46067Connes, Alain 28 1990 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 28 2013 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 27 2010 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 27 2001 Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067Connes, A.; Cuntz, J. 27 1988 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 26 2012 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006Connes, Alain; Moscovici, Henri 25 2000 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 25 2007 Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006Connes, Alain; Moscovici, Henri 25 1993 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034Connes, Alain; Shlyakhtenko, Dimitri 25 2005 Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069Connes, A.; Gromov, M.; Moscovici, H. 24 1993 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 24 2007 Approximately transitive flows and ITPFI factors. Zbl 0606.46041Connes, A.; Woods, E. J. 24 1985 KMS states and complex multiplication. Zbl 1106.58005Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 24 2005 Quantized calculus and applications. Zbl 1052.46510Connes, Alain 24 1995 Fun with \(\mathbb F_1\). Zbl 1228.11143Connes, Alain; Consani, Caterina; Marcolli, Matilde 24 2009 Scale invariance in the spectral action. Zbl 1112.83036Chamseddine, Ali H.; Connes, Alain 23 2006 The arithmetic site. (Le site arithmétique.) Zbl 1315.11054Connes, Alain; Consani, Caterina 23 2014 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 23 2011 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 23 2008 Factors of type \(III_ 1\), property \(L_{\lambda}'\) and closure of inner automorphisms. Zbl 0597.46063Connes, A. 22 1985 Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Zbl 0840.57013Connes, Alain; Sullivan, Dennis; Teleman, Nicolas 22 1994 Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023Connes, Alain; Moscovici, Henri 21 2004 Classification des facteurs. Zbl 0503.46043Connes, A. 21 1982 Tolerance relations and operator systems. Zbl 07614112Connes, Alain; van Suijlekom, Walter D. 1 2022 Spectral truncations in noncommutative geometry and operator systems. Zbl 1475.46062Connes, Alain; van Suijlekom, Walter Daniël 13 2021 On absolute algebraic geometry the affine case. Zbl 1478.14047Connes, Alain; Consani, Caterina 1 2021 Noncommutative geometry, the spectral standpoint. Zbl 07425826Connes, Alain 1 2021 Quasi-inner functions and local factors. Zbl 1476.46071Connes, Alain; Consani, Caterina 1 2021 Entropy and the spectral action. Zbl 1444.46049Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 6 2020 \(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061Connes, Alain; Consani, Caterina 3 2020 The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008Connes, Alain; Fathizadeh, Farzad 9 2019 Homological algebra in characteristic one. Zbl 1411.18006Connes, Alain; Consani, Caterina 8 2019 Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D. 7 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 The Riemann-Roch strategy. Complex lift of the scaling site. Zbl 1458.11108Connes, Alain; Consani, Caterina 1 2019 Geometry and the quantum. Zbl 1411.58003Connes, Alain 1 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 20 2016 Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046Connes, Alain; Consani, Caterina 10 2016 The scaling site. (Le site des fréquences.) Zbl 1348.18004Connes, Alain; Consani, Caterina 6 2016 An essay on the Riemann hypothesis. Zbl 1353.11095Connes, Alain 5 2016 Grand unification in the spectral Pati-Salam model. Zbl 1388.81965Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 18 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 55 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 14 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 81 2013 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 31 2013 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 28 2013 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 26 2012 Spectral action for Robertson-Walker metrics. Zbl 1397.81413Chamseddine, Ali H.; Connes, Alain 13 2012 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 49 2011 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 38 2011 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 23 2011 Characteristic 1, entropy and the absolute point. Zbl 1273.11140Connes, Alain; Consani, Caterina 20 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 Noncommutative geometry. Abstracts from the workshop held September 11–17, 2011. Zbl 1349.00115 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 The BC-system and \(L\)-functions. Zbl 1276.14002Connes, Alain 1 2011 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 52 2010 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 29 2010 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 27 2010 The uncanny precision of the spectral action. Zbl 1192.58005Chamseddine, Ali H.; Connes, Alain 20 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 13 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 105 2008 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 74 2008 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 55 2008 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 51 2008 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 23 2008 Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres. Zbl 1159.58003Connes, Alain; Dubois-Violette, Michel 9 2008 A unitary invariant in Riemannian geometry. Zbl 1197.46030Connes, Alain 4 2008 Gravity and the standard model with neutrino mixing. Zbl 1140.81022Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 128 2007 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 25 2007 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 24 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 15 2007 Yang-Mills and some related algebras. Zbl 1177.58009Connes, Alain; Dubois-Violette, Michel 9 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. 208 2006 Scale invariance in the spectral action. Zbl 1112.83036Chamseddine, Ali H.; Connes, Alain 23 2006 From physics to number theory via noncommutative geometry. 2nd printing. Zbl 1126.58006Connes, Alain; Marcolli, Matilde 19 2006 Inner fluctuations of the spectral action. Zbl 1105.58004Connes, Alain; Chamseddine, Ali H. 18 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 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 25 2005 KMS states and complex multiplication. Zbl 1106.58005Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 24 2005 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 45 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 6 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 99 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. 18 2002 Noncommutative geometry year 2000. Zbl 1138.58304Connes, Alain 5 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 110 2001 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 27 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 1015.81042Connes, A.; Kreimer, D. 4 2001 From local perturbation theory to Hopf and Lie algebras of Feynman graphs. Zbl 0995.81077Connes, Alain; Kreimer, Dirk 3 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 232 2000 ...and 133 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,550 Authors 87 Connes, Alain 56 Sukochev, Fedor Anatol’evich 52 Marcolli, Matilde 49 Guo, Li 46 Popa, Sorin Teodor 40 van Suijlekom, Walter Daniël 35 Landi, Giovanni 33 Majid, Shahn 33 Rennie, Adam 33 Sitarz, Andrzej 31 Dabrowski, Ludwik 29 Carey, Alan L. 29 Iochum, Bruno 29 Khalkhali, Masoud 29 Longo, Roberto 29 Vaes, Stefaan 28 Houdayer, Cyril 26 Martinetti, Pierre 25 Ponge, Raphaël S. 25 Yu, Guoliang 24 Benameur, Moulay-Tahar 24 Chamseddine, Ali Hani 24 Neshveyev, Sergey V. 24 Wang, Yong 24 Zanin, Dmitriy V. 23 Consani, Caterina 23 Ebrahimi-Fard, Kurusch 23 Haagerup, Uffe Valentin 23 Laca, Marcelo 23 Lizzi, Fedele 23 Mathai, Varghese 23 Skandalis, Georges 22 Jørgensen, Palle E. T. 21 D’Andrea, Francesco 21 Golodets, Valentin Yakovlevich 21 Goswami, Debashish 21 Ioana, Adrian 20 Gao, Xing 20 Kaad, Jens 19 Cho, Ilwoo 19 Narnhofer, Heide 19 Schücker, Thomas 19 Wulkenhaar, Raimar 18 Dubois-Violette, Michel 18 Foissy, Loïc 17 Bai, Chengming 17 Brzeziński, Tomasz 17 Junge, Marius 17 Latrémolière, Frédéric 17 Lorscheid, Oliver 17 Moscovici, Henri 17 Nest, Ryszard 17 Rangipour, Bahram 17 Størmer, Erling 17 Thomsen, Klaus E. 16 Manchon, Dominique 15 Bhowmick, Jyotishman 15 Chakraborty, Partha Sarathi 15 Chifan, Ionuţ 15 Choda, Marie 15 Dadarlat, Marius 15 Elliott, George A. 15 Nistor, Victor 15 Takesaki, Masamichi 15 Voiculescu, Dan-Virgil 15 Wallet, Jean-Christophe 15 Xia, Jingbo 14 Cuntz, Joachim 14 Fathizadeh, Farzad 14 Gracia-Bondía, José M. 14 Klimek, Slawomir 14 Patras, Frédéric 14 Paycha, Sylvie 14 Schrohe, Elmar 14 Schulz-Baldes, Hermann 14 Stephan, Christoph A. 13 Christensen, Erik 13 Fidaleo, Francesco 13 Jones, Vaughan Frederick Randal 13 Lesniewski, Andrzej 13 Savin, Anton Yur’evich 13 Sims, Aidan 13 Tomatsu, Reiji 13 Usachev, Aleksandr Sergeevich 13 Várilly, Joseph C. 12 Aastrup, Johannes 12 Bellissard, Jean V. 12 Gayral, Victor 12 Grosse, Harald 12 Hochs, Peter 12 Iovane, Gerardo 12 Isono, Yusuke 12 Kishimoto, Akitaka 12 Marrakchi, Amine 12 Masuda, Toshihiko 12 Mesland, Bram 12 Meyer, Ralf 12 Raeburn, Iain 12 Shlyakhtenko, Dimitri L. 12 Tang, Xiang ...and 3,450 more Authors all top 5 Cited in 402 Serials 398 Journal of Functional Analysis 334 Communications in Mathematical Physics 239 Journal of Geometry and Physics 194 Advances in Mathematics 186 Journal of Mathematical Physics 169 Journal of Noncommutative Geometry 157 Letters in Mathematical Physics 113 Proceedings of the American Mathematical Society 99 Transactions of the American Mathematical Society 86 Nuclear Physics. 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Series A 12 Topology and its Applications 12 Journal of the American Mathematical Society 12 Journal of the Australian Mathematical Society 11 Publications Mathématiques 11 Journal of Soviet Mathematics 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 Bulletin of the Australian Mathematical Society 10 Manuscripta Mathematica 10 Linear Algebra and its Applications 10 Nuclear Physics. B. Proceedings Supplements 10 Geometry & Topology 10 Algebras and Representation Theory 10 Journal of Homotopy and Related Structures 9 Studia Mathematica 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 9 Annals of Mathematics. Second Series 9 Physical Review Letters 9 Forum of Mathematics, Sigma 9 Annals of \(K\)-Theory ...and 302 more Serials all top 5 Cited in 62 Fields 2,382 Functional analysis (46-XX) 1,331 Quantum theory (81-XX) 1,045 Global analysis, analysis on manifolds (58-XX) 626 Associative rings and algebras (16-XX) 516 \(K\)-theory (19-XX) 453 Operator theory (47-XX) 415 Topological groups, Lie groups (22-XX) 399 Differential geometry (53-XX) 383 Nonassociative rings and algebras (17-XX) 353 Dynamical systems and ergodic theory (37-XX) 341 Relativity and gravitational theory (83-XX) 307 Group theory and generalizations (20-XX) 281 Category theory; homological algebra (18-XX) 258 Number theory (11-XX) 208 Algebraic geometry (14-XX) 204 Manifolds and cell complexes (57-XX) 186 Combinatorics (05-XX) 180 Measure and integration (28-XX) 177 Algebraic topology (55-XX) 159 Statistical mechanics, structure of matter (82-XX) 129 Abstract harmonic analysis (43-XX) 109 Partial differential equations (35-XX) 107 Probability theory and stochastic processes (60-XX) 73 Mathematical logic and foundations (03-XX) 64 Commutative algebra (13-XX) 60 Linear and multilinear algebra; matrix theory (15-XX) 60 Several complex variables and analytic spaces (32-XX) 56 General topology (54-XX) 51 Order, lattices, ordered algebraic structures (06-XX) 47 Information and communication theory, circuits (94-XX) 44 Field theory and polynomials (12-XX) 39 Ordinary differential equations (34-XX) 35 Functions of a complex variable (30-XX) 35 Computer science (68-XX) 34 Geometry (51-XX) 34 Mechanics of particles and systems (70-XX) 33 Harmonic analysis on Euclidean spaces (42-XX) 32 Convex and discrete geometry (52-XX) 30 General and overarching topics; collections (00-XX) 20 General algebraic systems (08-XX) 20 Numerical analysis (65-XX) 19 Special functions (33-XX) 17 History and biography (01-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Statistics (62-XX) 10 Real functions (26-XX) 10 Sequences, series, summability (40-XX) 10 Optics, electromagnetic theory (78-XX) 10 Operations research, mathematical programming (90-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Approximations and expansions (41-XX) 9 Astronomy and astrophysics (85-XX) 8 Difference and functional equations (39-XX) 7 Potential theory (31-XX) 6 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) 3 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Mechanics of deformable solids (74-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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