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Author ID: connes.alain Recent zbMATH articles by "Connes, Alain"
Published as: Connes, Alain; Connes, A.
Homepage: https://alainconnes.org/
External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr
Awards: Fields Medal (1982) · Clay Research Award (2000)
Member of Collective: Bourbaki, Nicolas
all top 5

Co-Authors

113 single-authored
40 Consani, Caterina
27 Moscovici, Henri
19 Chamseddine, Ali Hani
16 Marcolli, Matilde
9 Kreimer, Dirk
7 Cuntz, Joachim
7 Yu, Guoliang
6 Baum, Paul Frank
6 Gromov, Mikhael Leonidovich
6 Rieffel, Marc A.
6 van Suijlekom, Walter Daniël
5 Dubois-Violette, Michel
4 Alon, Noga
4 Bourgain, Jean
4 Milman, Vitali D.
4 Størmer, Erling
4 Woods, Edward James
3 Changeux, Jean-Pierre
3 Evans, David E.
3 Jones, Vaughan Frederick Randal
3 Karoubi, Max
3 Nest, Ryszard
3 Skandalis, Georges
3 Sukochev, Fedor Anatol’evich
3 Takesaki, Masamichi
3 Zanin, Dmitriy V.
2 Bost, Jean-Benoît
2 Douglas, Michael R.
2 Haagerup, Uffe Valentin
2 Higson, Nigel
2 Jaffe, Arthur Michael
2 Lichnerowicz, Andre
2 Lott, John
2 McDonald, Edward Andrew
2 Mukhanov, Viatcheslav F.
2 Narnhofer, Heide
2 Nikolaus, Thomas
2 Ramachandran, Niranjan
2 Schützenberger, Marcel-Paul
2 Schwarz, Albert S.
2 Shlyakhtenko, Dimitri L.
2 Sullivan, Dennis Parnell
2 Teleman, Nicolae Sinel
2 Weiss, Benjamin
1 Atiyah, Michael Francis
1 Barnsley, Michael Fielding
1 Baxter, Rodney J.
1 Birman, Joan S.
1 Bisch, Dietmar H.
1 Blum, Lenore
1 Bowen, Ray M.
1 Brézin, Edouard
1 Brown, Larry
1 Bryant, Robert L.
1 Burns, Daniel M. jun.
1 Caramello, Olivia
1 Cartier, Pierre
1 Cheeger, Jeff
1 Coburn, Lewis A.
1 Conder, Marston Donald Edward
1 Damour, Thibault
1 de la Harpe, Pierre
1 Dehen, Michele
1 Donnelly, Harold
1 Duflo, Michel
1 Dundas, Bjørn Ian
1 Ebin, David G.
1 Ellwood, David Alexandre
1 Fack, Thierry
1 Fathizadeh, Farzad
1 Fauvet, Frédéric
1 Fayet, Pierre
1 Feldman, Jacob
1 Flato, Moshé
1 Freedman, Michael Hartley
1 Fröhlich, Jürg Martin
1 Gallavotti, Giovanni M.
1 Gawȩdzki, Krzysztof
1 Glashow, Sheldon Lee
1 Goodman, Fred J.
1 Gorokhovsky, Alexander
1 Griffiths, Phillip Augustus
1 Guillemin, Victor W.
1 Guionnet, Alice
1 Helffer, Bernard
1 Helton, John William
1 Howe, Roger Evans
1 Hutchins, Shana
1 Izumi, Masaki
1 Jaeck, Frédéric
1 Jørgensen, Palle E. T.
1 Joseph, Anthony
1 Kaminker, Jerome
1 Kawahigashi, Yasuyuki
1 Khalkhali, Masoud
1 Kirby, Robion Cromwell
1 Kishimoto, Aki
1 Kouneiher, Joseph
1 Krieger, Wolfgang
1 Lafforgue, Laurent
...and 55 more Co-Authors
all top 5

Serials

18 Communications in Mathematical Physics
13 Comptes Rendus de l’Académie des Sciences. Série I
12 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A
9 Letters in Mathematical Physics
9 Oberwolfach Reports
8 Journal of Geometry and Physics
7 Journal of Functional Analysis
7 Journal of High Energy Physics
6 Notices of the American Mathematical Society
5 Journal of Number Theory
5 Selecta Mathematica. New Series
4 Advances in Mathematics
4 Ergodic Theory and Dynamical Systems
3 Journal of Mathematical Physics
3 Journal of Operator Theory
3 Annals of Mathematics. Second Series
3 Physical Review Letters
2 Acta Scientiarum Mathematicarum
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Bulletin of the London Mathematical Society
2 Tôhoku Mathematical Journal. Second Series
2 Topology
2 \(K\)-Theory
2 Geometric and Functional Analysis. GAFA
2 L’Enseignement Mathématique. 2e Série
2 Bulletin of the American Mathematical Society. New Series
2 Nuclear Physics. B. Proceedings Supplements
2 Moscow Mathematical Journal
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Journal of Noncommutative Geometry
2 Modern Birkhäuser Classics
1 American Mathematical Monthly
1 Classical and Quantum Gravity
1 Israel Journal of Mathematics
1 Nuclear Physics. B
1 Fortschritte der Physik
1 Acta Mathematica
1 Annales de l’Institut Fourier
1 Bulletin des Sciences Mathématiques. Deuxième Série
1 Canadian Mathematical Bulletin
1 Compositio Mathematica
1 Gazette des Mathématiciens
1 Illinois Journal of Mathematics
1 Publications Mathématiques
1 Journal of Pure and Applied Algebra
1 Journal für die Reine und Angewandte Mathematik
1 Mathematica Scandinavica
1 Nagoya Mathematical Journal
1 Pacific Journal of Mathematics
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Rendiconti del Seminario Matematico della Università di Padova
1 Journal of the American Mathematical Society
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 IMRN. International Mathematics Research Notices
1 Elemente der Mathematik
1 Journal of Algebraic Geometry
1 Journal de Théorie des Nombres de Bordeaux
1 Bulletin des Sciences Mathématiques
1 Theory and Applications of Categories
1 Matematicheskaya Fizika, Analiz, Geometriya
1 Sbornik: Mathematics
1 Documenta Mathematica
1 European Mathematical Society Newsletter
1 Advances in Theoretical and Mathematical Physics
1 Annales Henri Poincaré
1 The Quarterly Journal of Mathematics
1 Journal of the Institute of Mathematics of Jussieu
1 International Journal of Geometric Methods in Modern Physics
1 Bulletin of the American Mathematical Society
1 Astérisque
1 Colloquium Publications. American Mathematical Society
1 Contemporary Mathematics
1 Proceedings of Symposia in Pure Mathematics
1 Progress in Mathematics
1 Texts and Readings in Mathematics
1 SMF Journée Annuelle
1 IRMA Lectures in Mathematics and Theoretical Physics
1 Journal of Mathematics and Music
1 Münster Journal of Mathematics
1 Journal of \(K\)-Theory
1 Japanese Journal of Mathematics. 3rd Series
1 EMS Surveys in Mathematical Sciences
1 Higher Structures
1 Les Grandes Voix de la Recherche
1 Nouvelles Visions des Sciences

Publications by Year

Citations contained in zbMATH Open

241 Publications have been cited 10,860 times in 5,663 Documents Cited by Year
Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076
Connes, Alain
804
1994
Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042
Connes, Alain
424
1976
Non-commutative differential geometry. Zbl 0592.46056
Connes, Alain
352
1985
Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004
Connes, A.
317
1987
Une classification des facteurs de type III. Zbl 0274.46050
Connes, Alain
294
1973
Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem. Zbl 1032.81026
Connes, Alain; Kreimer, Dirk
281
2000
Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038
Connes, Alain; Kreimer, Dirk
273
1998
Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009
Connes, Alain
266
1996
On the foundations of noncommutative geometry. Zbl 1106.58004
Connes, A.
222
2006
The spectral action principle. Zbl 0894.58007
Chamseddine, Ali H.; Connes, Alain
218
1997
The local index formula in noncommutative geometry. Zbl 0960.46048
Connes, A.; Moscovici, H.
213
1995
An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018
Connes, A.; Feldman, J.; Weiss, B.
207
1981
Noncommutative geometry and reality. Zbl 0871.58008
Connes, Alain
181
1995
Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061
Baum, Paul; Connes, Alain; Higson, Nigel
163
1994
Gravity and the standard model with neutrino mixing. Zbl 1140.81022
Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde
149
2007
The longitudinal index theorem for foliations. Zbl 0575.58030
Connes, A.; Skandalis, G.
147
1984
Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047
Connes, Alain; Moscovici, Henri
146
1990
An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043
Connes, A.
132
1981
The action functional in non-commutative geometry. Zbl 0658.53068
Connes, A.
131
1988
Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051
Connes, A.
131
1989
Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005
Connes, A.; Moscovici, H.
129
1998
Noncommutative geometry, quantum fields and motives. Zbl 1209.58007
Connes, Alain; Marcolli, Matilde
128
2008
Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040
Bost, J.-B.; Connes, A.
127
1995
Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045
Connes, Alain; Landi, Giovanni
121
2001
Non-commutative geometry and physics. Zbl 0933.46069
Connes, A.
120
1995
Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059
Connes, Alain; Kreimer, Dirk
119
2001
Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052
Connes, Alain
119
1975
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015
Connes, Alain
112
1999
The flow of weights on factors of type III. Zbl 0408.46047
Connes, Alain; Takesaki, Masamichi
112
1977
C* algèbres et géométrie différentielle. Zbl 0433.46057
Connes, Alain
112
1980
Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009
Connes, Alain
111
1983
Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052
Connes, Alain; Douglas, Michael R.; Schwarz, Albert
107
1998
Property \(T\) for von Neumann algebras. Zbl 1190.46047
Connes, A.; Jones, V.
105
1985
Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005
Connes, Alain; Dubois-Violette, Michel
102
2002
Almost periodic states and factors of type III\(_1\). Zbl 0302.46050
Connes, A.
99
1974
On the spectral characterization of manifolds. Zbl 1287.58004
Connes, Alain
98
2013
Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073
Connes, A.; Narnhofer, H.; Thirring, W.
97
1987
A survey of foliations and operator algebras. Zbl 0531.57023
Connes, A.
92
1982
Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032
Connes, Alain; Størmer, Erling
83
1975
Noncommutative geometry, quantum fields and motives. Zbl 1159.58004
Connes, Alain; Marcolli, Matilde
83
2008
On the spatial theory of von Neumann algebras. Zbl 0443.46042
Connes, A.
81
1980
Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086
Connes, A.; Rovelli, C.
76
1994
Particle models and noncommutative geometry. Zbl 0957.46516
Connes, Alain; Lott, John
75
1990
Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505
Chamseddine, Ali H.; Connes, Alain
74
1996
Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078
Connes, Alain
73
1974
Deformations, asymptotic morphisms and bivariant \(K\)-theory. (Déformations, morphismes asymptotiques et \(K\)-théorie bivariante.) Zbl 0717.46062
Connes, Alain; Higson, Nigel
71
1990
Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049
Connes, A.
68
1988
Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027
Connes, A.
63
1977
Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001
Connes, Alain; Consani, Caterina
62
2010
Property T and asymptotically invariant sequences. Zbl 0479.28017
Connes, A.; Weiss, B.
61
1980
Why the standard model. Zbl 1140.81021
Chamseddine, Ali H.; Connes, Alain
59
2008
Geometry from the spectral point of view. Zbl 1042.46515
Connes, Alain
59
1995
Modular curvature for noncommutative two-tori. Zbl 1332.46070
Connes, Alain; Moscovici, Henri
59
2014
Sur la théorie non commutative de l’intégration. Zbl 0412.46053
Connes, Alain
58
1979
Type III and spectral triples. Zbl 1159.46041
Connes, Alain; Moscovici, Henri
57
2008
The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037
Connes, Alain; Tretkoff, Paula
54
2011
On the cohomology of operator algebras. Zbl 0408.46042
Connes, A.
54
1978
A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056
Connes, A.
52
1980
Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048
Connes, Alain; Størmer, Erling
51
1978
Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012
Connes, Alain
46
2004
Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042
Baum, Paul; Connes, Alain
45
2000
The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031
Connes, Alain; Moscovici, Henri
44
1982
Introduction to non commutative differential geometry. Zbl 0564.58002
Connes, A.
44
1985
Yang-Mills for non-commutative two-tori. Zbl 0633.46069
Connes, Alain; Rieffel, Marc A.
43
1987
The hyperring of adèle classes. Zbl 1221.14002
Connes, Alain; Consani, Caterina
43
2011
Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054
Connes, A.
40
1986
A factor not anti-isomorphic to itself. Zbl 0315.46058
Connes, A.
40
1975
Cyclic cohomology and Hopf algebras. Zbl 0941.16024
Connes, Alain; Moscovici, Henri
39
1999
A short survey of noncommutative geometry. Zbl 0974.58008
Connes, Alain
39
2000
Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
39
2013
Closed star products and cyclic cohomology. Zbl 0767.55005
Connes, Alain; Flato, Moshé; Sternheimer, Daniel
38
1992
Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024
Connes, Alain; Moscovici, Henri
36
2004
Noncommutative geometry. (Géométrie non commutative.) Zbl 0745.46067
Connes, Alain
35
1990
Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130
Chamseddine, Ali H.; Connes, Alain
35
2010
Resilience of the spectral standard model. Zbl 1397.81412
Chamseddine, Ali H.; Connes, Alain
34
2012
A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056
Connes, A.; Jones, V.
33
1982
Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
33
2013
Quantized calculus and applications. Zbl 1052.46510
Connes, Alain
32
1995
Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013
Connes, Alain; Krieger, Wolfgang
32
1977
From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002
Connes, Alain; Consani, Caterina
31
2010
Yang-Mills algebra. Zbl 1028.53025
Connes, Alain; Dubois-Violette, Michel
31
2002
Chern character for discrete groups. Zbl 0656.55005
Baum, Paul; Connes, Alain
30
1988
\(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034
Connes, Alain; Shlyakhtenko, Dimitri
30
2005
On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006
Connes, Alain; Consani, Caterina
30
2011
Classification des facteurs. Zbl 0503.46043
Connes, A.
28
1982
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013
Connes, Alain; Moscovici, Henri
28
2001
Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067
Connes, A.; Cuntz, J.
27
1988
Fun with \(\mathbb F_1\). Zbl 1228.11143
Connes, Alain; Consani, Caterina; Marcolli, Matilde
27
2009
KMS states and complex multiplication. Zbl 1106.58005
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
27
2005
Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001
Connes, Alain; Consani, Caterina; Marcolli, Matilde
26
2007
Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190
Chamseddine, Ali H.; Connes, Alain
26
2007
Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069
Connes, A.; Gromov, M.; Moscovici, H.
26
1993
Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Zbl 0840.57013
Connes, Alain; Sullivan, Dennis; Teleman, Nicolas
26
1994
The arithmetic site. (Le site arithmétique.) Zbl 1315.11054
Connes, Alain; Consani, Caterina
26
2014
Scale invariance in the spectral action. Zbl 1112.83036
Chamseddine, Ali H.; Connes, Alain
25
2006
A walk in the noncommutative garden. Zbl 1145.14005
Connes, Alain; Marcolli, Matilde
25
2008
Characteristic 1, entropy and the absolute point. Zbl 1273.11140
Connes, Alain; Consani, Caterina
25
2011
Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006
Connes, Alain; Moscovici, Henri
25
2000
Approximately transitive flows and ITPFI factors. Zbl 0606.46041
Connes, A.; Woods, E. J.
25
1985
Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006
Connes, Alain; Moscovici, Henri
25
1993
Spectral triples and \(\zeta\)-cycles. Zbl 07724321
Connes, Alain; Consani, Caterina
4
2023
Tolerance relations and operator systems. Zbl 07614112
Connes, Alain; van Suijlekom, Walter D.
3
2022
Spectral truncations in noncommutative geometry and operator systems. Zbl 1475.46062
Connes, Alain; van Suijlekom, Walter Daniël
22
2021
On absolute algebraic geometry the affine case. Zbl 1478.14047
Connes, Alain; Consani, Caterina
7
2021
Noncommutative geometry, the spectral standpoint. Zbl 1524.58003
Connes, Alain
4
2021
Weil positivity and trace formula the Archimedean place. Zbl 1480.46084
Connes, Alain; Consani, Caterina
4
2021
Segal’s gamma rings and universal arithmetic. Zbl 1484.14003
Connes, Alain; Consani, Caterina
4
2021
Memories of Vaughan Jones. Zbl 1480.01028
Bisch, Dietmar; Evans, David E.; Kirby, Robion; Popa, Sorin
3
2021
Quasi-inner functions and local factors. Zbl 1476.46071
Connes, Alain; Consani, Caterina
2
2021
The scaling Hamiltonian. Zbl 1524.11171
Connes, Alain; Consani, Caterina
1
2021
Entropy and the spectral action. Zbl 1444.46049
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
12
2020
\(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061
Connes, Alain; Consani, Caterina
6
2020
The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008
Connes, Alain; Fathizadeh, Farzad
13
2019
Homological algebra in characteristic one. Zbl 1411.18006
Connes, Alain; Consani, Caterina
11
2019
Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032
Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D.
8
2019
The Riemann-Roch strategy. Complex lift of the scaling site. Zbl 1458.11108
Connes, Alain; Consani, Caterina
3
2019
Noncommutative geometry for symmetric non-self-adjoint operators. Zbl 07063161
Connes, Alain; Levitina, Galina; McDonald, Edward; Sukochev, Fedor; Zanin, Dmitriy
2
2019
Sir Michael Atiyah, a knight mathematician: a tribute to Michael Atiyah, an inspiration and a friend. Zbl 1427.01016
Connes, Alain; Kouneiher, Joseph
1
2019
Ronald G. Douglas: a master in the art of transcending problems. Zbl 1427.01030
Yu, Guoliang; Howe, Roger; Hutchins, Shana
1
2019
Geometry and the quantum. Zbl 1411.58003
Connes, Alain
4
2018
Geometry of the scaling site. Zbl 1406.11118
Connes, Alain; Consani, Caterina
10
2017
Trace theorem for quasi-Fuchsian groups. Zbl 1455.30035
Connes, Alain; Sukochev, Fedor A.; Zanin, Dmitriy V.
7
2017
Geometry of the arithmetic site. Zbl 1368.14038
Connes, Alain; Consani, Caterina
23
2016
Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046
Connes, Alain; Consani, Caterina
14
2016
An essay on the Riemann hypothesis. Zbl 1353.11095
Connes, Alain
8
2016
The scaling site. (Le site des fréquences.) Zbl 1348.18004
Connes, Alain; Consani, Caterina
6
2016
Grand unification in the spectral Pati-Salam model. Zbl 1388.81965
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
20
2015
Universal thickening of the field of real numbers. Zbl 1387.11086
Connes, Alain; Consani, Caterina
14
2015
Cyclic structures and the topos of simplicial sets. Zbl 1328.19005
Connes, Alain; Consani, Caterina
9
2015
Projective geometry in characteristic one and the epicyclic category. Zbl 1338.19004
Connes, Alain; Consani, Caterina
7
2015
The cyclic and epicyclic sites. Zbl 1331.18005
Connes, Alain; Consani, Caterina
2
2015
Modular curvature for noncommutative two-tori. Zbl 1332.46070
Connes, Alain; Moscovici, Henri
59
2014
The arithmetic site. (Le site arithmétique.) Zbl 1315.11054
Connes, Alain; Consani, Caterina
26
2014
Geometry and the quantum: basics. Zbl 1333.81414
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
17
2014
On the arithmetic of the BC-system. Zbl 1302.11069
Connes, Alain; Consani, Caterina
9
2014
Cyclic homology, Serre’s local factors and \(\lambda\)-operations. Zbl 1327.14109
Connes, Alain; Consani, Caterina
6
2014
On the spectral characterization of manifolds. Zbl 1287.58004
Connes, Alain
98
2013
Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
39
2013
Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
33
2013
Resilience of the spectral standard model. Zbl 1397.81412
Chamseddine, Ali H.; Connes, Alain
34
2012
Spectral action for Robertson-Walker metrics. Zbl 1397.81413
Chamseddine, Ali H.; Connes, Alain
15
2012
The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037
Connes, Alain; Tretkoff, Paula
54
2011
The hyperring of adèle classes. Zbl 1221.14002
Connes, Alain; Consani, Caterina
43
2011
On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006
Connes, Alain; Consani, Caterina
30
2011
Characteristic 1, entropy and the absolute point. Zbl 1273.11140
Connes, Alain; Consani, Caterina
25
2011
The Witt construction in characteristic one and quantization. Zbl 1245.13015
Connes, Alain
10
2011
Noncommutative geometric spaces with boundary: spectral action. Zbl 1209.53061
Chamseddine, Ali H.; Connes, Alain
2
2011
Noncommutative geometry and global analysis. Conference in honor of Henri Moscovici, Bonn, Germany, June 29–July 4, 2009. Zbl 1218.00012
1
2011
Noncommutative geometry. Abstracts from the workshop held September 11–17, 2011. Zbl 1349.00115
1
2011
The BC-system and \(L\)-functions. Zbl 1276.14002
Connes, Alain
1
2011
Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001
Connes, Alain; Consani, Caterina
62
2010
Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. I. Zbl 1206.81130
Chamseddine, Ali H.; Connes, Alain
35
2010
From monoids to hyperstructures: in search of an absolute arithmetic. Zbl 1234.14002
Connes, Alain; Consani, Caterina
31
2010
The uncanny precision of the spectral action. Zbl 1192.58005
Chamseddine, Ali H.; Connes, Alain
23
2010
Visions in mathematics. GAFA 2000 special volume, Part II. Proceedings of the meeting “Visions in Mathematics – Towards 2000, Tel Aviv, Israel, August 25–September 3, 1999. Special volume of the journal Geometric and Functional Analysis – GAFA. Reprint of the 2000 original. Zbl 1185.00038
1
2010
Fun with \(\mathbb F_1\). Zbl 1228.11143
Connes, Alain; Consani, Caterina; Marcolli, Matilde
27
2009
The Weil proof and the geometry of the adelès class space. Zbl 1208.11108
Connes, Alain; Consani, Caterina; Marcolli, Matilde
14
2009
Renormalization and Galois theories. Selected papers of the CIRM workshop, Luminy, France, March 2006. Zbl 1173.14003
1
2009
Noncommutative geometry, quantum fields and motives. Zbl 1209.58007
Connes, Alain; Marcolli, Matilde
128
2008
Noncommutative geometry, quantum fields and motives. Zbl 1159.58004
Connes, Alain; Marcolli, Matilde
83
2008
Why the standard model. Zbl 1140.81021
Chamseddine, Ali H.; Connes, Alain
59
2008
Type III and spectral triples. Zbl 1159.46041
Connes, Alain; Moscovici, Henri
57
2008
A walk in the noncommutative garden. Zbl 1145.14005
Connes, Alain; Marcolli, Matilde
25
2008
Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres. Zbl 1159.58003
Connes, Alain; Dubois-Violette, Michel
10
2008
A unitary invariant in Riemannian geometry. Zbl 1197.46030
Connes, Alain
5
2008
Gravity and the standard model with neutrino mixing. Zbl 1140.81022
Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde
149
2007
Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001
Connes, Alain; Consani, Caterina; Marcolli, Matilde
26
2007
Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190
Chamseddine, Ali H.; Connes, Alain
26
2007
Quantum gravity boundary terms from the spectral action of noncommutative space. Zbl 1228.83080
Chamseddine, Ali H.; Connes, Alain
20
2007
Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory. Zbl 1200.81113
Connes, Alain; Marcolli, Matilde
16
2007
Yang-Mills and some related algebras. Zbl 1177.58009
Connes, Alain; Dubois-Violette, Michel
10
2007
A property of parallelograms inscribed in ellipses. Zbl 1140.51010
Connes, Alain; Zagier, Don
9
2007
Noncommutative geometry. Abstracts from the workshop held September 2–8, 2007. Zbl 1177.58003
2
2007
On the foundations of noncommutative geometry. Zbl 1106.58004
Connes, A.
222
2006
Scale invariance in the spectral action. Zbl 1112.83036
Chamseddine, Ali H.; Connes, Alain
25
2006
From physics to number theory via noncommutative geometry. 2nd printing. Zbl 1126.58006
Connes, Alain; Marcolli, Matilde
21
2006
Inner fluctuations of the spectral action. Zbl 1105.58004
Connes, Alain; Chamseddine, Ali H.
20
2006
Quantum fields and motives. Zbl 1092.81050
Connes, Alain; Marcolli, Matilde
13
2006
KMS states and complex multiplication. II. Zbl 1123.58004
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
9
2006
Noncommutative geometry and physics. Zbl 1129.83012
Connes, Alain
8
2006
\(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. Zbl 1139.58003
Connes, Alain; Marcolli, Matilde
4
2006
Morse inequalities for foliations. Zbl 1112.57007
Connes, Alain; Fack, Thierry
1
2006
Transgressions of the Godbillon-Vey class and Rademacher functions. Zbl 1109.11027
Connes, Alain; Moscovici, Henri
1
2006
\(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034
Connes, Alain; Shlyakhtenko, Dimitri
30
2005
KMS states and complex multiplication. Zbl 1106.58005
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
27
2005
Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012
Connes, Alain
46
2004
Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024
Connes, Alain; Moscovici, Henri
36
2004
Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023
Connes, Alain; Moscovici, Henri
21
2004
Renormalization and motivic Galois theory. Zbl 1131.81021
Connes, Alain; Marcolli, Matilde
9
2004
Cyclic cohomology, noncommutative geometry and quantum group symmetries. Zbl 1052.46057
Connes, Alain
7
2004
Renormalization and Galois ambiguity. (Renormalisation et ambiguïté galoisienne.) Zbl 1072.81045
Connes, Alain
1
2004
Moduli space and structure of noncommutative 3-spheres. Zbl 1052.58012
Connes, Alain; Dubois-Violette, Michel
17
2003
Galois symmetries and renormalization. (Symétries galoisiennes et renormalisation.) Zbl 1050.81052
Connes, Alain
1
2003
Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005
Connes, Alain; Dubois-Violette, Michel
102
2002
Yang-Mills algebra. Zbl 1028.53025
Connes, Alain; Dubois-Violette, Michel
31
2002
Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Zbl 1033.81061
Connes, A.; Kreimer, D.
18
2002
Noncommutative geometry year 2000. Zbl 1138.58304
Connes, Alain
6
2002
Hommage à Laurent Schwartz. Zbl 1015.01013
Connes, Alain
1
2002
Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045
Connes, Alain; Landi, Giovanni
121
2001
Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group. Zbl 1042.81059
Connes, Alain; Kreimer, Dirk
119
2001
...and 141 more Documents
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Cited by 4,011 Authors

93 Connes, Alain
66 Guo, Li
61 Sukochev, Fedor Anatol’evich
56 Marcolli, Matilde
48 Popa, Sorin Teodor
46 van Suijlekom, Walter Daniël
41 Majid, Shahn
38 Landi, Giovanni
35 Sitarz, Andrzej
34 Khalkhali, Masoud
33 Rennie, Adam
33 Vaes, Stefaan
32 Dabrowski, Ludwik
31 Wang, Yong
30 Houdayer, Cyril
30 Iochum, Bruno
30 Longo, Roberto
30 Yu, Guoliang
29 Carey, Alan L.
29 Gao, Xing
29 Zanin, Dmitriy V.
28 Martinetti, Pierre
27 Consani, Caterina
27 Ioana, Adrian
27 Ponge, Raphaël S.
26 Lizzi, Fedele
25 Benameur, Moulay-Tahar
25 Ebrahimi-Fard, Kurusch
25 Neshveyev, Sergey V.
24 Chamseddine, Ali Hani
24 Jørgensen, Palle E. T.
24 Mathai, Varghese
23 Cho, Ilwoo
23 Haagerup, Uffe Valentin
23 Kaad, Jens
23 Laca, Marcelo
23 Skandalis, Georges
22 Wulkenhaar, Raimar
21 D’Andrea, Francesco
21 Golodets, Valentin Yakovlevich
21 Goswami, Debashish
21 Latrémolière, Frédéric
21 Nest, Ryszard
21 Wallet, Jean-Christophe
20 Bai, Chengming
20 Foissy, Loïc
20 Lorscheid, Oliver
19 Dubois-Violette, Michel
19 Narnhofer, Heide
19 Schücker, Thomas
18 Brzeziński, Tomasz
18 Chifan, Ionuţ
18 Junge, Marius
18 Manchon, Dominique
18 Xia, Jingbo
17 Moscovici, Henri
17 Paycha, Sylvie
17 Rangipour, Bahram
17 Savin, Anton Yur’evich
17 Sheng, Yunhe
17 Størmer, Erling
16 Chakraborty, Partha Sarathi
16 Elliott, George A.
16 Jun, Jaiung
16 Voiculescu, Dan-Virgil
15 Bhowmick, Jyotishman
15 Choda, Marie
15 Dadarlat, Marius
15 Fidaleo, Francesco
15 Klimek, Slawomir
15 Nistor, Victor
15 Patras, Frédéric
15 Schulz-Baldes, Hermann
15 Shlyakhtenko, Dimitri L.
15 Takesaki, Masamichi
14 Aastrup, Johannes
14 Castro Perelman, Carlos
14 Cuntz, Joachim
14 Fathizadeh, Farzad
14 Gracia-Bondía, José M.
14 Grosse, Harald
14 Jones, Vaughan Frederick Randal
14 Meyer, Ralf
14 Schrohe, Elmar
14 Sims, Aidan
14 Stephan, Christoph A.
13 Christensen, Erik
13 Goffeng, Magnus
13 Guin, Satyajit
13 Hochs, Peter
13 Isono, Yusuke
13 Lesniewski, Andrzej
13 Marrakchi, Amine
13 Mesland, Bram
13 Tang, Xiang
13 Tomatsu, Reiji
13 Usachev, Aleksandr Sergeevich
13 Várilly, Joseph C.
13 Wang, Hang
13 Wang, Jian
...and 3,911 more Authors
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Cited in 431 Serials

418 Journal of Functional Analysis
347 Communications in Mathematical Physics
253 Journal of Geometry and Physics
212 Advances in Mathematics
210 Journal of Mathematical Physics
192 Journal of Noncommutative Geometry
161 Letters in Mathematical Physics
118 Proceedings of the American Mathematical Society
117 Journal of High Energy Physics
105 Transactions of the American Mathematical Society
92 Nuclear Physics. B
83 Journal of Algebra
75 \(K\)-Theory
73 Journal of Pure and Applied Algebra
71 Mathematische Annalen
64 Ergodic Theory and Dynamical Systems
62 International Journal of Mathematics
60 Publications of the Research Institute for Mathematical Sciences, Kyoto University
58 Inventiones Mathematicae
58 International Journal of Geometric Methods in Modern Physics
56 Journal of Mathematical Analysis and Applications
54 Comptes Rendus. Mathématique. Académie des Sciences, Paris
52 Reviews in Mathematical Physics
49 International Journal of Modern Physics A
49 International Journal of Theoretical Physics
44 Physics Letters. B
44 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
42 Israel Journal of Mathematics
42 Chaos, Solitons and Fractals
41 Journal für die Reine und Angewandte Mathematik
40 Journal of Physics A: Mathematical and Theoretical
34 Communications in Algebra
32 Annales de l’Institut Fourier
32 Bulletin of the American Mathematical Society. New Series
32 Journal of \(K\)-Theory
30 Annales Henri Poincaré
29 Journal of Number Theory
29 Mathematische Zeitschrift
27 Integral Equations and Operator Theory
25 General Relativity and Gravitation
25 Reports on Mathematical Physics
25 Mathematical Physics, Analysis and Geometry
24 Journal of Mathematical Sciences (New York)
24 Complex Analysis and Operator Theory
23 Geometric and Functional Analysis. GAFA
22 Rocky Mountain Journal of Mathematics
22 Acta Mathematica
22 Duke Mathematical Journal
22 Science China. Mathematics
21 Modern Physics Letters A
21 Journal of Algebra and its Applications
21 Groups, Geometry, and Dynamics
20 Russian Journal of Mathematical Physics
19 Classical and Quantum Gravity
19 Journal of Topology and Analysis
18 Memoirs of the American Mathematical Society
18 Documenta Mathematica
18 Foundations of Physics
17 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
17 Compositio Mathematica
17 Expositiones Mathematicae
17 Infinite Dimensional Analysis, Quantum Probability and Related Topics
17 Acta Mathematica Sinica. English Series
16 Journal d’Analyse Mathématique
16 Annals of Physics
16 Journal of Algebraic Combinatorics
16 Advances in Applied Clifford Algebras
15 Physics Letters. A
15 Bulletin of the London Mathematical Society
15 Tôhoku Mathematical Journal. Second Series
15 Topology and its Applications
15 Selecta Mathematica. New Series
15 Bulletin des Sciences Mathématiques
15 Algebras and Representation Theory
14 Mathematical Proceedings of the Cambridge Philosophical Society
14 Journal of the London Mathematical Society. Second Series
14 Applied Categorical Structures
14 Journal of Pseudo-Differential Operators and Applications
13 Mathematical Notes
13 Bulletin de la Société Mathématique de France
13 Functional Analysis and its Applications
13 Acta Applicandae Mathematicae
13 Journal of the Australian Mathematical Society
12 Bulletin of the Australian Mathematical Society
12 Proceedings of the Japan Academy. Series A
12 Journal of the American Mathematical Society
12 Journal of Homotopy and Related Structures
12 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
12 Annals of \(K\)-Theory
11 Studia Mathematica
11 Publications Mathématiques
11 Journal of Soviet Mathematics
11 Linear Algebra and its Applications
11 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
11 Geometry & Topology
11 Banach Journal of Mathematical Analysis
11 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics
11 Forum of Mathematics, Sigma
10 Manuscripta Mathematica
10 Nuclear Physics. B. Proceedings Supplements
...and 331 more Serials
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Cited in 62 Fields

2,596 Functional analysis (46-XX)
1,513 Quantum theory (81-XX)
1,151 Global analysis, analysis on manifolds (58-XX)
699 Associative rings and algebras (16-XX)
552 \(K\)-theory (19-XX)
518 Operator theory (47-XX)
468 Topological groups, Lie groups (22-XX)
463 Differential geometry (53-XX)
440 Nonassociative rings and algebras (17-XX)
400 Relativity and gravitational theory (83-XX)
388 Dynamical systems and ergodic theory (37-XX)
345 Group theory and generalizations (20-XX)
324 Category theory; homological algebra (18-XX)
282 Number theory (11-XX)
252 Algebraic geometry (14-XX)
226 Manifolds and cell complexes (57-XX)
212 Combinatorics (05-XX)
200 Algebraic topology (55-XX)
186 Measure and integration (28-XX)
177 Statistical mechanics, structure of matter (82-XX)
145 Abstract harmonic analysis (43-XX)
135 Partial differential equations (35-XX)
127 Probability theory and stochastic processes (60-XX)
85 Mathematical logic and foundations (03-XX)
78 Commutative algebra (13-XX)
75 Several complex variables and analytic spaces (32-XX)
71 Linear and multilinear algebra; matrix theory (15-XX)
60 Order, lattices, ordered algebraic structures (06-XX)
60 General topology (54-XX)
55 Information and communication theory, circuits (94-XX)
50 Field theory and polynomials (12-XX)
46 Ordinary differential equations (34-XX)
46 Geometry (51-XX)
45 Mechanics of particles and systems (70-XX)
44 Harmonic analysis on Euclidean spaces (42-XX)
41 Functions of a complex variable (30-XX)
40 Computer science (68-XX)
39 General and overarching topics; collections (00-XX)
38 Convex and discrete geometry (52-XX)
25 Numerical analysis (65-XX)
23 General algebraic systems (08-XX)
23 Special functions (33-XX)
22 History and biography (01-XX)
18 Statistics (62-XX)
15 Real functions (26-XX)
15 Classical thermodynamics, heat transfer (80-XX)
13 Difference and functional equations (39-XX)
13 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
12 Optics, electromagnetic theory (78-XX)
12 Operations research, mathematical programming (90-XX)
10 Sequences, series, summability (40-XX)
10 Approximations and expansions (41-XX)
9 Potential theory (31-XX)
9 Calculus of variations and optimal control; optimization (49-XX)
9 Astronomy and astrophysics (85-XX)
6 Systems theory; control (93-XX)
5 Integral transforms, operational calculus (44-XX)
5 Integral equations (45-XX)
3 Fluid mechanics (76-XX)
3 Biology and other natural sciences (92-XX)
2 Mathematics education (97-XX)
1 Mechanics of deformable solids (74-XX)

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