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Author ID: connes.alain Recent zbMATH articles by "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
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
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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

Publications by Year

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 0818.46076
Connes, Alain
609
1994
Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042
Connes, Alain
352
1976
Non-commutative differential geometry. Zbl 0592.46056
Connes, Alain
310
1985
Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004
Connes, A.
267
1987
Une classification des facteurs de type III. Zbl 0274.46050
Connes, Alain
262
1973
Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009
Connes, Alain
233
1996
Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038
Connes, 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 1032.81026
Connes, Alain; Kreimer, Dirk
217
2000
On the foundations of noncommutative geometry. Zbl 1106.58004
Connes, A.
202
2006
An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018
Connes, A.; Feldman, J.; Weiss, B.
189
1981
The local index formula in noncommutative geometry. Zbl 0960.46048
Connes, A.; Moscovici, H.
188
1995
The spectral action principle. Zbl 0894.58007
Chamseddine, Ali H.; Connes, Alain
185
1997
Noncommutative geometry and reality. Zbl 0871.58008
Connes, Alain
147
1995
The longitudinal index theorem for foliations. Zbl 0575.58030
Connes, A.; Skandalis, G.
137
1984
Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061
Baum, Paul; Connes, Alain; Higson, Nigel
129
1994
Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047
Connes, Alain; Moscovici, Henri
128
1990
An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043
Connes, A.
122
1981
Gravity and the standard model with neutrino mixing. Zbl 1140.81022
Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde
119
2007
Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005
Connes, A.; Moscovici, H.
118
1998
Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040
Bost, J.-B.; Connes, A.
118
1995
Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045
Connes, Alain; Landi, Giovanni
112
2001
Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052
Connes, Alain
109
1975
Non-commutative geometry and physics. Zbl 0933.46069
Connes, A.
108
1995
Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051
Connes, A.
107
1989
The action functional in non-commutative geometry. Zbl 0658.53068
Connes, A.
107
1988
The flow of weights on factors of type III. Zbl 0408.46047
Connes, 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 1042.81059
Connes, Alain; Kreimer, Dirk
105
2001
Noncommutative geometry, quantum fields and motives. Zbl 1209.58007
Connes, Alain; Marcolli, Matilde
100
2008
Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009
Connes, Alain
98
1983
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015
Connes, Alain
96
1999
Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005
Connes, Alain; Dubois-Violette, Michel
96
2002
Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073
Connes, A.; Narnhofer, H.; Thirring, W.
93
1987
C* algèbres et géométrie différentielle. Zbl 0433.46057
Connes, Alain
91
1980
Almost periodic states and factors of type III\(_1\). Zbl 0302.46050
Connes, A.
89
1974
Property \(T\) for von Neumann algebras. Zbl 1190.46047
Connes, A.; Jones, V.
86
1985
Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052
Connes, Alain; Douglas, Michael R.; Schwarz, Albert
79
1998
Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032
Connes, Alain; Størmer, Erling
77
1975
On the spatial theory of von Neumann algebras. Zbl 0443.46042
Connes, A.
75
1980
On the spectral characterization of manifolds. Zbl 1287.58004
Connes, Alain
73
2013
Noncommutative geometry, quantum fields and motives. Zbl 1159.58004
Connes, Alain; Marcolli, Matilde
71
2008
Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078
Connes, Alain
66
1974
A survey of foliations and operator algebras. Zbl 0531.57023
Connes, A.
65
1982
Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049
Connes, A.
64
1988
Deformations, asymptotic morphisms and bivariant \(K\)-theory. (Déformations, morphismes asymptotiques et \(K\)-théorie bivariante.) Zbl 0717.46062
Connes, Alain; Higson, Nigel
64
1990
Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086
Connes, A.; Rovelli, C.
62
1994
Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505
Chamseddine, Ali H.; Connes, Alain
59
1996
Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027
Connes, A.
56
1977
Particle models and noncommutative geometry. Zbl 0957.46516
Connes, Alain; Lott, John
55
1990
Why the standard model. Zbl 1140.81021
Chamseddine, Ali H.; Connes, Alain
55
2008
Geometry from the spectral point of view. Zbl 1042.46515
Connes, Alain
53
1995
Modular curvature for noncommutative two-tori. Zbl 1332.46070
Connes, Alain; Moscovici, Henri
50
2014
A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056
Connes, A.
50
1980
Property T and asymptotically invariant sequences. Zbl 0479.28017
Connes, A.; Weiss, B.
50
1980
Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001
Connes, Alain; Consani, Caterina
50
2010
On the cohomology of operator algebras. Zbl 0408.46042
Connes, A.
49
1978
Type III and spectral triples. Zbl 1159.46041
Connes, Alain; Moscovici, Henri
47
2008
The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037
Connes, Alain; Tretkoff, Paula
46
2011
Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048
Connes, Alain; Størmer, Erling
46
1978
Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012
Connes, Alain
44
2004
Sur la théorie non commutative de l’intégration. Zbl 0412.46053
Connes, Alain
41
1979
Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042
Baum, Paul; Connes, Alain
40
2000
Introduction to non commutative differential geometry. Zbl 0564.58002
Connes, A.
40
1985
The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031
Connes, Alain; Moscovici, Henri
40
1982
The hyperring of adèle classes. Zbl 1221.14002
Connes, Alain; Consani, Caterina
37
2011
Yang-Mills for non-commutative two-tori. Zbl 0633.46069
Connes, Alain; Rieffel, Marc A.
37
1987
A factor not anti-isomorphic to itself. Zbl 0315.46058
Connes, A.
37
1975
Cyclic cohomology and Hopf algebras. Zbl 0941.16024
Connes, Alain; Moscovici, Henri
36
1999
Closed star products and cyclic cohomology. Zbl 0767.55005
Connes, Alain; Flato, Moshé; Sternheimer, Daniel
36
1992
A short survey of noncommutative geometry. Zbl 0974.58008
Connes, Alain
35
2000
A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056
Connes, A.; Jones, V.
32
1982
Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054
Connes, A.
32
1986
Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024
Connes, Alain; Moscovici, Henri
31
2004
Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013
Connes, Alain; Krieger, Wolfgang
30
1977
Yang-Mills algebra. Zbl 1028.53025
Connes, Alain; Dubois-Violette, Michel
29
2002
Noncommutative geometry. (Géométrie non commutative.) Zbl 0745.46067
Connes, Alain
28
1990
Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130
Chamseddine, Ali H.; Connes, Alain
28
2010
Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
26
2013
Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067
Connes, A.; Cuntz, J.
26
1988
From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002
Connes, Alain; Consani, Caterina
26
2010
Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006
Connes, Alain; Moscovici, Henri
25
1993
Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001
Connes, Alain; Consani, Caterina; Marcolli, Matilde
25
2007
\(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034
Connes, Alain; Shlyakhtenko, Dimitri
24
2005
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013
Connes, Alain; Moscovici, Henri
24
2001
Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006
Connes, Alain; Moscovici, Henri
24
2000
Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069
Connes, A.; Gromov, M.; Moscovici, H.
24
1993
Approximately transitive flows and ITPFI factors. Zbl 0606.46041
Connes, A.; Woods, E. J.
24
1985
KMS states and complex multiplication. Zbl 1106.58005
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
24
2005
Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190
Chamseddine, Ali H.; Connes, Alain
24
2007
Scale invariance in the spectral action. Zbl 1112.83036
Chamseddine, Ali H.; Connes, Alain
23
2006
The arithmetic site. (Le site arithmétique.) Zbl 1315.11054
Connes, Alain; Consani, Caterina
22
2014
Quantized calculus and applications. Zbl 1052.46510
Connes, Alain
22
1995
Fun with \(\mathbb F_1\). Zbl 1228.11143
Connes, Alain; Consani, Caterina; Marcolli, Matilde
22
2009
Resilience of the spectral standard model. Zbl 1397.81412
Chamseddine, Ali H.; Connes, Alain
22
2012
A walk in the noncommutative garden. Zbl 1145.14005
Connes, Alain; Marcolli, Matilde
22
2008
Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
22
2013
Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023
Connes, Alain; Moscovici, Henri
21
2004
Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Zbl 0840.57013
Connes, Alain; Sullivan, Dennis; Teleman, Nicolas
21
1994
Classification des facteurs. Zbl 0503.46043
Connes, A.
21
1982
Factors of type \(III_ 1\), property \(L_{\lambda}'\) and closure of inner automorphisms. Zbl 0597.46063
Connes, A.
21
1985
Chern character for discrete groups. Zbl 0656.55005
Baum, Paul; Connes, Alain
21
1988
Spectral truncations in noncommutative geometry and operator systems. Zbl 1475.46062
Connes, Alain; van Suijlekom, Walter Daniël
6
2021
Quasi-inner functions and local factors. Zbl 1476.46071
Connes, Alain; Consani, Caterina
1
2021
On absolute algebraic geometry the affine case. Zbl 1478.14047
Connes, Alain; Consani, Caterina
1
2021
Entropy and the spectral action. Zbl 1444.46049
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
4
2020
\(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061
Connes, Alain; Consani, Caterina
3
2020
Homological algebra in characteristic one. Zbl 1411.18006
Connes, Alain; Consani, Caterina
8
2019
The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008
Connes, Alain; Fathizadeh, Farzad
7
2019
Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032
Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D.
6
2019
Noncommutative geometry for symmetric non-self-adjoint operators. Zbl 07063161
Connes, Alain; Levitina, Galina; McDonald, Edward; Sukochev, Fedor; Zanin, Dmitriy
2
2019
Sir Michael Atiyah, a knight mathematician: a tribute to Michael Atiyah, an inspiration and a friend. Zbl 1427.01016
Connes, Alain; Kouneiher, Joseph
1
2019
Ronald G. Douglas: a master in the art of transcending problems. Zbl 1427.01030
Yu, Guoliang; Howe, Roger; Hutchins, Shana
1
2019
The Riemann-Roch strategy. Complex lift of the scaling site. Zbl 1458.11108
Connes, Alain; Consani, Caterina
1
2019
Geometry and the quantum. Zbl 1411.58003
Connes, Alain
1
2018
Geometry of the scaling site. Zbl 1406.11118
Connes, Alain; Consani, Caterina
8
2017
Trace theorem for quasi-Fuchsian groups. Zbl 1455.30035
Connes, Alain; Sukochev, Fedor A.; Zanin, Dmitriy V.
5
2017
Geometry of the arithmetic site. Zbl 1368.14038
Connes, Alain; Consani, Caterina
19
2016
Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046
Connes, Alain; Consani, Caterina
9
2016
The scaling site. (Le site des fréquences.) Zbl 1348.18004
Connes, Alain; Consani, Caterina
6
2016
An essay on the Riemann hypothesis. Zbl 1353.11095
Connes, Alain
5
2016
Grand unification in the spectral Pati-Salam model. Zbl 1388.81965
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
16
2015
Universal thickening of the field of real numbers. Zbl 1387.11086
Connes, Alain; Consani, Caterina
14
2015
Projective geometry in characteristic one and the epicyclic category. Zbl 1338.19004
Connes, Alain; Consani, Caterina
7
2015
Cyclic structures and the topos of simplicial sets. Zbl 1328.19005
Connes, Alain; Consani, Caterina
6
2015
The cyclic and epicyclic sites. Zbl 1331.18005
Connes, Alain; Consani, Caterina
2
2015
Modular curvature for noncommutative two-tori. Zbl 1332.46070
Connes, Alain; Moscovici, Henri
50
2014
The arithmetic site. (Le site arithmétique.) Zbl 1315.11054
Connes, Alain; Consani, Caterina
22
2014
Geometry and the quantum: basics. Zbl 1333.81414
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
13
2014
On the arithmetic of the BC-system. Zbl 1302.11069
Connes, Alain; Consani, Caterina
7
2014
Cyclic homology, Serre’s local factors and \(\lambda\)-operations. Zbl 1327.14109
Connes, Alain; Consani, Caterina
6
2014
On the spectral characterization of manifolds. Zbl 1287.58004
Connes, Alain
73
2013
Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
26
2013
Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
22
2013
Resilience of the spectral standard model. Zbl 1397.81412
Chamseddine, Ali H.; Connes, Alain
22
2012
Spectral action for Robertson-Walker metrics. Zbl 1397.81413
Chamseddine, Ali H.; Connes, Alain
13
2012
The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037
Connes, Alain; Tretkoff, Paula
46
2011
The hyperring of adèle classes. Zbl 1221.14002
Connes, Alain; Consani, Caterina
37
2011
Characteristic 1, entropy and the absolute point. Zbl 1273.11140
Connes, Alain; Consani, Caterina
20
2011
On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006
Connes, Alain; Consani, Caterina
19
2011
The Witt construction in characteristic one and quantization. Zbl 1245.13015
Connes, Alain
8
2011
Noncommutative geometric spaces with boundary: spectral action. Zbl 1209.53061
Chamseddine, Ali H.; Connes, Alain
2
2011
The BC-system and \(L\)-functions. Zbl 1276.14002
Connes, 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 1201.14001
Connes, Alain; Consani, Caterina
50
2010
Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130
Chamseddine, Ali H.; Connes, Alain
28
2010
From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002
Connes, Alain; Consani, Caterina
26
2010
The uncanny precision of the spectral action. Zbl 1192.58005
Chamseddine, 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 1228.11143
Connes, Alain; Consani, Caterina; Marcolli, Matilde
22
2009
The Weil proof and the geometry of the adelès class space. Zbl 1208.11108
Connes, 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 1209.58007
Connes, Alain; Marcolli, Matilde
100
2008
Noncommutative geometry, quantum fields and motives. Zbl 1159.58004
Connes, Alain; Marcolli, Matilde
71
2008
Why the standard model. Zbl 1140.81021
Chamseddine, Ali H.; Connes, Alain
55
2008
Type III and spectral triples. Zbl 1159.46041
Connes, Alain; Moscovici, Henri
47
2008
A walk in the noncommutative garden. Zbl 1145.14005
Connes, Alain; Marcolli, Matilde
22
2008
Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres. Zbl 1159.58003
Connes, Alain; Dubois-Violette, Michel
9
2008
A unitary invariant in Riemannian geometry. Zbl 1197.46030
Connes, Alain
4
2008
Gravity and the standard model with neutrino mixing. Zbl 1140.81022
Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde
119
2007
Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001
Connes, Alain; Consani, Caterina; Marcolli, Matilde
25
2007
Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190
Chamseddine, Ali H.; Connes, Alain
24
2007
Quantum gravity boundary terms from the spectral action of noncommutative space. Zbl 1228.83080
Chamseddine, Ali H.; Connes, Alain
17
2007
Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory. Zbl 1200.81113
Connes, Alain; Marcolli, Matilde
15
2007
Yang-Mills and some related algebras. Zbl 1177.58009
Connes, Alain; Dubois-Violette, Michel
9
2007
A property of parallelograms inscribed in ellipses. Zbl 1140.51010
Connes, 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 1106.58004
Connes, A.
202
2006
Scale invariance in the spectral action. Zbl 1112.83036
Chamseddine, Ali H.; Connes, Alain
23
2006
From physics to number theory via noncommutative geometry. 2nd printing. Zbl 1126.58006
Connes, Alain; Marcolli, Matilde
20
2006
Inner fluctuations of the spectral action. Zbl 1105.58004
Connes, Alain; Chamseddine, Ali H.
17
2006
Quantum fields and motives. Zbl 1092.81050
Connes, Alain; Marcolli, Matilde
13
2006
Noncommutative geometry and physics. Zbl 1129.83012
Connes, Alain
8
2006
KMS states and complex multiplication. II. Zbl 1123.58004
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
8
2006
\(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. Zbl 1139.58003
Connes, Alain; Marcolli, Matilde
4
2006
Transgressions of the Godbillon-Vey class and Rademacher functions. Zbl 1109.11027
Connes, Alain; Moscovici, Henri
1
2006
Morse inequalities for foliations. Zbl 1112.57007
Connes, Alain; Fack, Thierry
1
2006
\(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034
Connes, Alain; Shlyakhtenko, Dimitri
24
2005
KMS states and complex multiplication. Zbl 1106.58005
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
24
2005
Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012
Connes, Alain
44
2004
Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024
Connes, Alain; Moscovici, Henri
31
2004
Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023
Connes, Alain; Moscovici, Henri
21
2004
Renormalization and motivic Galois theory. Zbl 1131.81021
Connes, Alain; Marcolli, Matilde
9
2004
Cyclic cohomology, noncommutative geometry and quantum group symmetries. Zbl 1052.46057
Connes, Alain
6
2004
Renormalization and Galois ambiguity. (Renormalisation et ambiguïté galoisienne.) Zbl 1072.81045
Connes, Alain
1
2004
Moduli space and structure of noncommutative 3-spheres. Zbl 1052.58012
Connes, Alain; Dubois-Violette, Michel
16
2003
Galois symmetries and renormalization. (Symétries galoisiennes et renormalisation.) Zbl 1050.81052
Connes, Alain
1
2003
Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005
Connes, Alain; Dubois-Violette, Michel
96
2002
Yang-Mills algebra. Zbl 1028.53025
Connes, Alain; Dubois-Violette, Michel
29
2002
Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Zbl 1033.81061
Connes, A.; Kreimer, D.
16
2002
Noncommutative geometry year 2000. Zbl 1138.58304
Connes, Alain
5
2002
Hommage à Laurent Schwartz. Zbl 1015.01013
Connes, Alain
1
2002
Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045
Connes, Alain; Landi, Giovanni
112
2001
Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059
Connes, Alain; Kreimer, Dirk
105
2001
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013
Connes, Alain; Moscovici, Henri
24
2001
Triangle of thoughts. Translated from the French by Jennifer Gage. Zbl 1015.00005
Connes, Alain; Lichnerowicz, André; Schützenberger, Marcel Paul
4
2001
From local perturbation theory to Hopf- and Lie-algebras of Feynman graphs. Zbl 1015.81042
Connes, A.; Kreimer, D.
3
2001
From local perturbation theory to Hopf and Lie algebras of Feynman graphs. Zbl 0995.81077
Connes, 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 1032.81026
Connes, Alain; Kreimer, Dirk
217
2000
Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042
Baum, Paul; Connes, Alain
40
2000
A short survey of noncommutative geometry. Zbl 0974.58008
Connes, Alain
35
2000
Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006
Connes, Alain; Moscovici, Henri
24
2000
...and 129 more Documents
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
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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
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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)

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