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: 259 Publications since 1969, including 11 Books 19 Contributions as Editor · 4 Further Contributions Biographic References: 6 Publications Co-Authors: 79 Co-Authors with 173 Joint Publications 2,940 Co-Co-Authors all top 5 Co-Authors 108 single-authored 28 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 Yu, Guoliang 5 Dubois-Violette, Michel 5 van Suijlekom, Walter Daniël 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 Bowen, Ray M. 1 Brézin, Edouard 1 Brown, Larry 1 Coburn, Lewis A. 1 Conder, Marsteon 1 Damour, Thibault 1 de la Harpe, Pierre 1 Dehen, Michele 1 Duflo, Michel 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 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 1 Nikolaus, Thomas 1 Pflaum, Markus J. 1 Popa, Sorin Teodor 1 Ramis, Jean-Pierre 1 Ratcliffe, John G. 1 Rentschler, Rudolf 1 Reshetikhin, Nikolai Yu. 1 Rnagipour, Bahram ...and 16 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 Selecta Mathematica. New Series 4 Advances in Mathematics 4 Ergodic Theory and Dynamical Systems 4 Notices of the American Mathematical Society 3 Journal of Mathematical Physics 3 Annals of Mathematics. Second Series 3 Physical Review Letters 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Bulletin of the London Mathematical Society 2 Tohoku Mathematical Journal. Second Series 2 Topology 2 Journal of Operator Theory 2 \(K\)-Theory 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 Nuclear Physics. B. Proceedings Supplements 2 Moscow Mathematical Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Noncommutative Geometry 2 Modern Birkhäuser Classics 1 American Mathematical Monthly 1 Classical and Quantum Gravity 1 Israel Journal of Mathematics 1 Nuclear Physics. B 1 Fortschritte der Physik 1 Acta Mathematica 1 Acta Scientiarum Mathematicarum 1 Annales de l’Institut Fourier 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Canadian Mathematical Bulletin 1 Compositio Mathematica 1 Gazette des Mathématiciens 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Scandinavica 1 Nagoya Mathematical Journal 1 Pacific Journal of Mathematics 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti del Seminario Matematico della Università di Padova 1 Journal of the American Mathematical Society 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 IMRN. International Mathematics Research Notices 1 Elemente der Mathematik 1 L’Enseignement Mathématique. 2e Série 1 Journal of Algebraic Geometry 1 Journal de Théorie des Nombres de Bordeaux 1 Theory and Applications of Categories 1 Matematicheskaya Fizika, Analiz, Geometriya 1 Sbornik: Mathematics 1 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 153 Functional analysis (46-XX) 112 Global analysis, analysis on manifolds (58-XX) 72 Quantum theory (81-XX) 50 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 Nonassociative rings and algebras (17-XX) 11 Measure and integration (28-XX) 11 Relativity and gravitational theory (83-XX) 10 History and biography (01-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 229 Publications have been cited 9,197 times in 4,893 Documents Cited by ▼ Year ▼ Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076Connes, Alain 609 1994 Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042Connes, Alain 352 1976 Non-commutative differential geometry. Zbl 0592.46056Connes, Alain 310 1985 Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004Connes, A. 267 1987 Une classification des facteurs de type III. Zbl 0274.46050Connes, Alain 262 1973 Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009Connes, Alain 233 1996 Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038Connes, Alain; Kreimer, Dirk 226 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 217 2000 On the foundations of noncommutative geometry. Zbl 1106.58004Connes, A. 202 2006 An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018Connes, A.; Feldman, J.; Weiss, B. 189 1981 The local index formula in noncommutative geometry. Zbl 0960.46048Connes, A.; Moscovici, H. 188 1995 The spectral action principle. Zbl 0894.58007Chamseddine, Ali H.; Connes, Alain 185 1997 Noncommutative geometry and reality. Zbl 0871.58008Connes, Alain 147 1995 The longitudinal index theorem for foliations. Zbl 0575.58030Connes, A.; Skandalis, G. 137 1984 Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061Baum, Paul; Connes, Alain; Higson, Nigel 129 1994 Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047Connes, Alain; Moscovici, Henri 128 1990 An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043Connes, A. 122 1981 Gravity and the standard model with neutrino mixing. Zbl 1140.81022Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde 119 2007 Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005Connes, A.; Moscovici, H. 118 1998 Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040Bost, J.-B.; Connes, A. 118 1995 Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045Connes, Alain; Landi, Giovanni 112 2001 Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052Connes, Alain 109 1975 Non-commutative geometry and physics. Zbl 0933.46069Connes, A. 108 1995 Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051Connes, A. 107 1989 The action functional in non-commutative geometry. Zbl 0658.53068Connes, A. 107 1988 The flow of weights on factors of type III. Zbl 0408.46047Connes, Alain; Takesaki, Masamichi 107 1977 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 105 2001 Noncommutative geometry, quantum fields and motives. Zbl 1209.58007Connes, Alain; Marcolli, Matilde 100 2008 Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009Connes, Alain 98 1983 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015Connes, Alain 96 1999 Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005Connes, Alain; Dubois-Violette, Michel 96 2002 Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073Connes, A.; Narnhofer, H.; Thirring, W. 93 1987 C* algèbres et géométrie différentielle. Zbl 0433.46057Connes, Alain 91 1980 Almost periodic states and factors of type III\(_1\). Zbl 0302.46050Connes, A. 89 1974 Property \(T\) for von Neumann algebras. Zbl 1190.46047Connes, A.; Jones, V. 86 1985 Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052Connes, Alain; Douglas, Michael R.; Schwarz, Albert 79 1998 Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032Connes, Alain; Størmer, Erling 77 1975 On the spatial theory of von Neumann algebras. Zbl 0443.46042Connes, A. 75 1980 On the spectral characterization of manifolds. Zbl 1287.58004Connes, Alain 73 2013 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 71 2008 Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078Connes, Alain 66 1974 A survey of foliations and operator algebras. Zbl 0531.57023Connes, A. 65 1982 Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049Connes, A. 64 1988 Deformations, asymptotic morphisms and bivariant \(K\)-theory. (Déformations, morphismes asymptotiques et \(K\)-théorie bivariante.) Zbl 0717.46062Connes, Alain; Higson, Nigel 64 1990 Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086Connes, A.; Rovelli, C. 62 1994 Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505Chamseddine, Ali H.; Connes, Alain 59 1996 Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027Connes, A. 56 1977 Particle models and noncommutative geometry. Zbl 0957.46516Connes, Alain; Lott, John 55 1990 Why the standard model. Zbl 1140.81021Chamseddine, Ali H.; Connes, Alain 55 2008 Geometry from the spectral point of view. Zbl 1042.46515Connes, Alain 53 1995 Modular curvature for noncommutative two-tori. Zbl 1332.46070Connes, Alain; Moscovici, Henri 50 2014 A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056Connes, A. 50 1980 Property T and asymptotically invariant sequences. Zbl 0479.28017Connes, A.; Weiss, B. 50 1980 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 50 2010 On the cohomology of operator algebras. Zbl 0408.46042Connes, A. 49 1978 Type III and spectral triples. Zbl 1159.46041Connes, Alain; Moscovici, Henri 47 2008 The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037Connes, Alain; Tretkoff, Paula 46 2011 Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048Connes, Alain; Størmer, Erling 46 1978 Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012Connes, Alain 44 2004 Sur la théorie non commutative de l’intégration. Zbl 0412.46053Connes, Alain 41 1979 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042Baum, Paul; Connes, Alain 40 2000 Introduction to non commutative differential geometry. Zbl 0564.58002Connes, A. 40 1985 The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031Connes, Alain; Moscovici, Henri 40 1982 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 37 2011 Yang-Mills for non-commutative two-tori. Zbl 0633.46069Connes, Alain; Rieffel, Marc A. 37 1987 A factor not anti-isomorphic to itself. Zbl 0315.46058Connes, A. 37 1975 Cyclic cohomology and Hopf algebras. Zbl 0941.16024Connes, Alain; Moscovici, Henri 36 1999 Closed star products and cyclic cohomology. Zbl 0767.55005Connes, Alain; Flato, Moshé; Sternheimer, Daniel 36 1992 A short survey of noncommutative geometry. Zbl 0974.58008Connes, Alain 35 2000 A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056Connes, A.; Jones, V. 32 1982 Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054Connes, A. 32 1986 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 31 2004 Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013Connes, Alain; Krieger, Wolfgang 30 1977 Yang-Mills algebra. Zbl 1028.53025Connes, Alain; Dubois-Violette, Michel 29 2002 Noncommutative geometry. (Géométrie non commutative.) Zbl 0745.46067Connes, Alain 28 1990 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 28 2010 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 26 2013 Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067Connes, A.; Cuntz, J. 26 1988 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 26 2010 Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006Connes, Alain; Moscovici, Henri 25 1993 Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001Connes, Alain; Consani, Caterina; Marcolli, Matilde 25 2007 \(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034Connes, Alain; Shlyakhtenko, Dimitri 24 2005 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 24 2001 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006Connes, Alain; Moscovici, Henri 24 2000 Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069Connes, A.; Gromov, M.; Moscovici, H. 24 1993 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 Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190Chamseddine, Ali H.; Connes, Alain 24 2007 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 22 2014 Quantized calculus and applications. Zbl 1052.46510Connes, Alain 22 1995 Fun with \(\mathbb F_1\). Zbl 1228.11143Connes, Alain; Consani, Caterina; Marcolli, Matilde 22 2009 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 22 2012 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 22 2008 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 22 2013 Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023Connes, Alain; Moscovici, Henri 21 2004 Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Zbl 0840.57013Connes, Alain; Sullivan, Dennis; Teleman, Nicolas 21 1994 Classification des facteurs. Zbl 0503.46043Connes, A. 21 1982 Factors of type \(III_ 1\), property \(L_{\lambda}'\) and closure of inner automorphisms. Zbl 0597.46063Connes, A. 21 1985 Chern character for discrete groups. Zbl 0656.55005Baum, Paul; Connes, Alain 21 1988 Spectral truncations in noncommutative geometry and operator systems. Zbl 1475.46062Connes, Alain; van Suijlekom, Walter Daniël 6 2021 Quasi-inner functions and local factors. Zbl 1476.46071Connes, Alain; Consani, Caterina 1 2021 On absolute algebraic geometry the affine case. Zbl 1478.14047Connes, Alain; Consani, Caterina 1 2021 Entropy and the spectral action. Zbl 1444.46049Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 4 2020 \(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061Connes, Alain; Consani, Caterina 3 2020 Homological algebra in characteristic one. Zbl 1411.18006Connes, Alain; Consani, Caterina 8 2019 The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008Connes, Alain; Fathizadeh, Farzad 7 2019 Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D. 6 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. 5 2017 Geometry of the arithmetic site. Zbl 1368.14038Connes, Alain; Consani, Caterina 19 2016 Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046Connes, Alain; Consani, Caterina 9 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. 16 2015 Universal thickening of the field of real numbers. Zbl 1387.11086Connes, Alain; Consani, Caterina 14 2015 Projective geometry in characteristic one and the epicyclic category. Zbl 1338.19004Connes, Alain; Consani, Caterina 7 2015 Cyclic structures and the topos of simplicial sets. Zbl 1328.19005Connes, Alain; Consani, Caterina 6 2015 The cyclic and epicyclic sites. Zbl 1331.18005Connes, Alain; Consani, Caterina 2 2015 Modular curvature for noncommutative two-tori. Zbl 1332.46070Connes, Alain; Moscovici, Henri 50 2014 The arithmetic site. (Le site arithmétique.) Zbl 1315.11054Connes, Alain; Consani, Caterina 22 2014 Geometry and the quantum: basics. Zbl 1333.81414Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav 13 2014 On the arithmetic of the BC-system. Zbl 1302.11069Connes, Alain; Consani, Caterina 7 2014 Cyclic homology, Serre’s local factors and \(\lambda\)-operations. Zbl 1327.14109Connes, Alain; Consani, Caterina 6 2014 On the spectral characterization of manifolds. Zbl 1287.58004Connes, Alain 73 2013 Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D. 26 2013 Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D. 22 2013 Resilience of the spectral standard model. Zbl 1397.81412Chamseddine, Ali H.; Connes, Alain 22 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 46 2011 The hyperring of adèle classes. Zbl 1221.14002Connes, Alain; Consani, Caterina 37 2011 Characteristic 1, entropy and the absolute point. Zbl 1273.11140Connes, Alain; Consani, Caterina 20 2011 On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006Connes, Alain; Consani, Caterina 19 2011 The Witt construction in characteristic one and quantization. Zbl 1245.13015Connes, Alain 8 2011 Noncommutative geometric spaces with boundary: spectral action. Zbl 1209.53061Chamseddine, Ali H.; Connes, Alain 2 2011 The BC-system and \(L\)-functions. Zbl 1276.14002Connes, Alain 1 2011 Noncommutative geometry and global analysis. Conference in honor of Henri Moscovici, Bonn, Germany, June 29–July 4, 2009. Zbl 1218.00012 1 2011 Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001Connes, Alain; Consani, Caterina 50 2010 Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130Chamseddine, Ali H.; Connes, Alain 28 2010 From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002Connes, Alain; Consani, Caterina 26 2010 The uncanny precision of the spectral action. Zbl 1192.58005Chamseddine, Ali H.; Connes, Alain 19 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 22 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 100 2008 Noncommutative geometry, quantum fields and motives. Zbl 1159.58004Connes, Alain; Marcolli, Matilde 71 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 47 2008 A walk in the noncommutative garden. Zbl 1145.14005Connes, Alain; Marcolli, Matilde 22 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 119 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 5 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. 202 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 20 2006 Inner fluctuations of the spectral action. Zbl 1105.58004Connes, Alain; Chamseddine, Ali H. 17 2006 Quantum fields and motives. Zbl 1092.81050Connes, Alain; Marcolli, Matilde 13 2006 Noncommutative geometry and physics. Zbl 1129.83012Connes, Alain 8 2006 KMS states and complex multiplication. II. Zbl 1123.58004Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan 8 2006 \(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. Zbl 1139.58003Connes, Alain; Marcolli, Matilde 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 24 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 44 2004 Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024Connes, Alain; Moscovici, Henri 31 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 16 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 96 2002 Yang-Mills algebra. Zbl 1028.53025Connes, Alain; Dubois-Violette, Michel 29 2002 Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Zbl 1033.81061Connes, A.; Kreimer, D. 16 2002 Noncommutative geometry year 2000. Zbl 1138.58304Connes, Alain 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 112 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 105 2001 Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013Connes, Alain; Moscovici, Henri 24 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. 3 2001 From local perturbation theory to Hopf and Lie algebras of Feynman graphs. Zbl 0995.81077Connes, Alain; Kreimer, Dirk 2 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 217 2000 Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042Baum, Paul; Connes, Alain 40 2000 A short survey of noncommutative geometry. Zbl 0974.58008Connes, Alain 35 2000 Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006Connes, Alain; Moscovici, Henri 24 2000 ...and 129 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,408 Authors 87 Connes, Alain 52 Marcolli, Matilde 52 Sukochev, Fedor Anatol’evich 46 Guo, Li 45 Popa, Sorin Teodor 37 van Suijlekom, Walter Daniël 33 Landi, Giovanni 33 Majid, Shahn 32 Rennie, Adam 31 Sitarz, Andrzej 29 Dabrowski, Ludwik 29 Iochum, Bruno 29 Khalkhali, Masoud 29 Longo, Roberto 28 Carey, Alan L. 27 Houdayer, Cyril 27 Vaes, Stefaan 25 Martinetti, Pierre 25 Yu, Guoliang 24 Neshveyev, Sergey V. 24 Ponge, Raphaël S. 23 Benameur, Moulay-Tahar 23 Consani, Caterina 23 Haagerup, Uffe Valentin 23 Laca, Marcelo 23 Skandalis, Georges 23 Wang, Yong 22 Chamseddine, Ali Hani 22 Ebrahimi-Fard, Kurusch 22 Zanin, Dmitriy V. 21 Golodets, Valentin Yakovlevich 21 Goswami, Debashish 21 Ioana, Adrian 21 Jørgensen, Palle E. T. 21 Lizzi, Fedele 21 Mathai, Varghese 20 D’Andrea, Francesco 19 Cho, Ilwoo 19 Gao, Xing 19 Narnhofer, Heide 19 Schücker, Thomas 19 Wulkenhaar, Raimar 18 Dubois-Violette, Michel 18 Foissy, Loïc 18 Kaad, Jens 17 Bai, Chengming 17 Brzeziński, Tomasz 17 Latrémolière, Frédéric 17 Lorscheid, Oliver 17 Moscovici, Henri 17 Nest, Ryszard 17 Rangipour, Bahram 17 Størmer, Erling 17 Thomsen, Klaus E. 16 Junge, Marius 16 Manchon, Dominique 15 Bhowmick, Jyotishman 15 Chakraborty, Partha Sarathi 15 Choda, Marie 15 Elliott, George A. 15 Nistor, Victor 15 Takesaki, Masamichi 15 Voiculescu, Dan-Virgil 15 Wallet, Jean-Christophe 14 Cuntz, Joachim 14 Dadarlat, Marius 14 Fathizadeh, Farzad 14 Gracia-Bondía, José M. 14 Schulz-Baldes, Hermann 14 Stephan, Christoph A. 13 Chifan, Ionuţ 13 Christensen, Erik 13 Klimek, Slawomir 13 Lesniewski, Andrzej 13 Patras, Frédéric 13 Paycha, Sylvie 13 Sims, Aidan 13 Tomatsu, Reiji 13 Várilly, Joseph C. 12 Aastrup, Johannes 12 Bellissard, Jean V. 12 Fidaleo, Francesco 12 Gayral, Victor 12 Grosse, Harald 12 Iovane, Gerardo 12 Isono, Yusuke 12 Jones, Vaughan Frederick Randal 12 Kishimoto, Akitaka 12 Marrakchi, Amine 12 Mesland, Bram 12 Meyer, Ralf 12 Raeburn, Iain 12 Schrohe, Elmar 12 Shlyakhtenko, Dimitri L. 12 Tang, Xiang 12 Usachev, Aleksandr Sergeevich 12 Winter, Wilhelm 12 Xia, Jingbo 11 Bieliavsky, Pierre 11 Emerson, Heath ...and 3,308 more Authors all top 5 Cited in 390 Serials 388 Journal of Functional Analysis 327 Communications in Mathematical Physics 235 Journal of Geometry and Physics 191 Advances in Mathematics 183 Journal of Mathematical Physics 159 Journal of Noncommutative Geometry 154 Letters in Mathematical Physics 109 Proceedings of the American Mathematical Society 97 Transactions of the American Mathematical Society 83 Nuclear Physics. B 75 \(K\)-Theory 71 Journal of Algebra 68 Journal of High Energy Physics 65 Mathematische Annalen 63 Journal of Pure and Applied Algebra 61 Ergodic Theory and Dynamical Systems 60 Publications of the Research Institute for Mathematical Sciences, Kyoto University 57 Inventiones Mathematicae 56 International Journal of Mathematics 53 Journal of Mathematical Analysis and Applications 49 International Journal of Modern Physics A 49 Comptes Rendus. Mathématique. Académie des Sciences, Paris 47 International Journal of Geometric Methods in Modern Physics 46 Reviews in Mathematical Physics 45 International Journal of Theoretical Physics 43 Physics Letters. B 38 Journal für die Reine und Angewandte Mathematik 37 Israel Journal of Mathematics 37 Chaos, Solitons and Fractals 33 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 32 Journal of \(K\)-Theory 30 Annales de l’Institut Fourier 29 Communications in Algebra 29 Bulletin of the American Mathematical Society. New Series 26 Journal of Number Theory 26 Annales Henri Poincaré 25 Integral Equations and Operator Theory 24 General Relativity and Gravitation 24 Reports on Mathematical Physics 22 Rocky Mountain Journal of Mathematics 22 Acta Mathematica 22 Mathematische Zeitschrift 22 Geometric and Functional Analysis. GAFA 21 Modern Physics Letters A 21 Duke Mathematical Journal 20 Journal of Mathematical Sciences (New York) 20 Mathematical Physics, Analysis and Geometry 19 Groups, Geometry, and Dynamics 19 Science China. Mathematics 18 Russian Journal of Mathematical Physics 18 Journal of Algebra and its Applications 17 Expositiones Mathematicae 16 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 16 Memoirs of the American Mathematical Society 16 Infinite Dimensional Analysis, Quantum Probability and Related Topics 16 Acta Mathematica Sinica. English Series 16 Complex Analysis and Operator Theory 15 Annals of Physics 15 Foundations of Physics 14 Mathematical Proceedings of the Cambridge Philosophical Society 14 Tohoku Mathematical Journal. Second Series 14 Journal of Algebraic Combinatorics 14 Applied Categorical Structures 14 Advances in Applied Clifford Algebras 13 Classical and Quantum Gravity 13 Journal d’Analyse Mathématique 13 Compositio Mathematica 13 Acta Applicandae Mathematicae 13 Selecta Mathematica. New Series 13 Bulletin des Sciences Mathématiques 13 Journal of Topology and Analysis 13 Journal of Pseudo-Differential Operators and Applications 12 Mathematical Notes 12 Physics Letters. A 12 Functional Analysis and its Applications 12 Proceedings of the Japan Academy. Series A 12 Journal of the American Mathematical Society 12 Documenta Mathematica 12 Journal of the Australian Mathematical Society 11 Bulletin de la Société Mathématique de France 11 Publications Mathématiques 11 Journal of Soviet Mathematics 11 Topology and its Applications 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 Journal of Homotopy and Related Structures 9 Differential Geometry and its Applications 9 Annales de l’Institut Henri Poincaré. Physique Théorique 9 Geometry & Topology 9 Algebras and Representation Theory 9 Physical Review Letters 9 Forum of Mathematics, Sigma 8 Studia Mathematica 8 Archiv der Mathematik 8 Monatshefte für Mathematik 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série ...and 290 more Serials all top 5 Cited in 62 Fields 2,307 Functional analysis (46-XX) 1,279 Quantum theory (81-XX) 1,007 Global analysis, analysis on manifolds (58-XX) 599 Associative rings and algebras (16-XX) 489 \(K\)-theory (19-XX) 430 Operator theory (47-XX) 400 Topological groups, Lie groups (22-XX) 386 Differential geometry (53-XX) 369 Nonassociative rings and algebras (17-XX) 335 Dynamical systems and ergodic theory (37-XX) 334 Relativity and gravitational theory (83-XX) 288 Group theory and generalizations (20-XX) 270 Category theory; homological algebra (18-XX) 251 Number theory (11-XX) 205 Algebraic geometry (14-XX) 201 Manifolds and cell complexes (57-XX) 182 Combinatorics (05-XX) 175 Measure and integration (28-XX) 173 Algebraic topology (55-XX) 154 Statistical mechanics, structure of matter (82-XX) 125 Abstract harmonic analysis (43-XX) 102 Partial differential equations (35-XX) 101 Probability theory and stochastic processes (60-XX) 67 Mathematical logic and foundations (03-XX) 63 Commutative algebra (13-XX) 57 Several complex variables and analytic spaces (32-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 54 General topology (54-XX) 49 Order, lattices, ordered algebraic structures (06-XX) 44 Field theory and polynomials (12-XX) 44 Information and communication theory, circuits (94-XX) 39 Ordinary differential equations (34-XX) 34 Mechanics of particles and systems (70-XX) 33 Harmonic analysis on Euclidean spaces (42-XX) 33 Computer science (68-XX) 32 Functions of a complex variable (30-XX) 31 Convex and discrete geometry (52-XX) 30 General and overarching topics; collections (00-XX) 30 Geometry (51-XX) 20 Special functions (33-XX) 19 General algebraic systems (08-XX) 18 Numerical analysis (65-XX) 17 History and biography (01-XX) 11 Classical thermodynamics, heat transfer (80-XX) 10 Real functions (26-XX) 10 Statistics (62-XX) 10 Optics, electromagnetic theory (78-XX) 10 Operations research, mathematical programming (90-XX) 9 Difference and functional equations (39-XX) 9 Astronomy and astrophysics (85-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Sequences, series, summability (40-XX) 7 Approximations and expansions (41-XX) 6 Potential theory (31-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Integral transforms, operational calculus (44-XX) 5 Integral equations (45-XX) 5 Systems theory; control (93-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. Updates and corrections should be made in Wikidata.