×

zbMATH — the first resource for mathematics

Connes, Alain

Compute Distance To:
Author ID: connes.alain Recent zbMATH articles by "Connes, Alain"
Published as: Connes, A.; Connes, Alain
Homepage: http://www.alainconnes.org/en/
External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor
Awards: Fields Medal (1982) · Clay Research Award (2000)
Member of Collective: Bourbaki, Nicolas
Documents Indexed: 272 Publications since 1969, including 21 Books
Biographic References: 6 Publications
all top 5

Co-Authors

106 single-authored
25 Consani, Caterina
21 Moscovici, Henri
18 Chamseddine, Ali Hani
14 Marcolli, Matilde
9 Kreimer, Dirk
7 Cuntz, Joachim
6 Gromov, Mikhael Leonidovich
6 Rieffel, Marc A.
5 Baum, Paul Frank
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
4 Yu, Guoliang
3 Changeux, Jean-Pierre
3 Jones, Vaughan Frederick Randal
3 Karoubi, Max
3 Sukochev, Fedor Anatol’evich
3 Takesaki, Masamichi
3 Zanin, Dmitriy V.
2 Bost, Jean-Benoît
2 Higson, Nigel
2 Lichnerowicz, Andre
2 Lott, John
2 Mcdonald, Edward A.
2 Ramachandran, Niranjan
2 Schützenberger, Marcel-Paul
2 Schwarz, Albert S.
2 Skandalis, Georges
2 Sullivan, Dennis Parnell
2 Teleman, Nicolae Sinel
2 Weiss, Benjamin
1 Atiyah, Michael Francis
1 Brézin, Edouard
1 Brodskiĭ, Ya. S.
1 Damour, Thibault
1 Douglas, Michael R.
1 Duflo, Michel
1 Ellwood, David Alexandre
1 Evans, David E.
1 Fack, Thierry
1 Fathizadeh, Farzad
1 Fauvet, Frédéric
1 Fayet, Pierre
1 Feldman, Jacob
1 Flato, Moshé
1 Fröhlich, Jürg Martin
1 Gawȩdzki, Krzysztof
1 Gorokhovsky, Alexander
1 Haagerup, Uffe Valentin
1 Helffer, Bernard
1 Joseph, Anthony
1 Kouneiher, Joseph
1 Krieger, Wolfgang
1 Landi, Giovanni
1 Lebowitz, Joel Louis
1 Lesch, Matthias
1 Levitina, Galina
1 Mukhanov, Viatcheslav F.
1 Musat, Magdalena
1 Narnhofer, Heide
1 Nest, Ryszard
1 Pflaum, Markus J.
1 Ramis, Jean-Pierre
1 Rentschler, Rudolf
1 Rnagipour, Bahram
1 Rørdam, Mikael
1 Rovelli, Carlo
1 Schick, Thomas
1 Shlyakhtenko, Dimitri L.
1 Sternheimer, Daniel
1 Thirring, Walter E.
1 Tretkoff, Paula
1 Vaes, Stefaan
1 Van Daele, Alfons
1 Zagier, Don Bernard
1 Zinn-Justin, Jean
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
7 Journal of Functional Analysis
7 Journal of High Energy Physics
7 Oberwolfach Reports
5 Journal of Number Theory
4 Ergodic Theory and Dynamical Systems
4 Selecta Mathematica. New Series
3 Journal of Mathematical Physics
3 Advances in Mathematics
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 Notices of the American Mathematical Society
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 European Mathematical Society Newsletter
1 Advances in Theoretical and Mathematical Physics
1 Annales Henri Poincaré
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 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

223 Publications have been cited 9,490 times in 4,775 Documents Cited by Year
Noncommutative geometry. Transl. from the French by Sterling Berberian. Zbl 0818.46076
Connes, Alain
792
1994
Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\). Zbl 0343.46042
Connes, Alain
379
1976
Non-commutative differential geometry. Zbl 0592.46056
Connes, Alain
338
1985
Cyclic cohomology and noncommutative differential geometry. Zbl 0681.55004
Connes, A.
333
1987
Une classification des facteurs de type III. Zbl 0274.46050
Connes, Alain
257
1973
Gravity coupled with matter and the foundation of non-commutative geometry. Zbl 0881.58009
Connes, Alain
231
1996
On the foundations of noncommutative geometry. Zbl 1106.58004
Connes, A.
221
2006
Hopf algebras, renormalization and noncommutative geometry. Zbl 0932.16038
Connes, Alain; Kreimer, Dirk
208
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
192
2000
The spectral action principle. Zbl 0894.58007
Chamseddine, Ali H.; Connes, Alain
188
1997
The local index formula in noncommutative geometry. Zbl 0960.46048
Connes, A.; Moscovici, H.
182
1995
Noncommutative geometry and matrix theory: Compactification on tori. Zbl 1018.81052
Connes, Alain; Douglas, Michael R.; Schwarz, Albert
178
1998
An amenable equivalence relation is generated by a single transformation. Zbl 0491.28018
Connes, A.; Feldman, J.; Weiss, B.
178
1981
Noncommutative geometry and reality. Zbl 0871.58008
Connes, Alain
139
1995
The longitudinal index theorem for foliations. Zbl 0575.58030
Connes, A.; Skandalis, G.
125
1984
Classifying space for proper actions and \(K\)-theory of group \(C^*\)- algebras. Zbl 0830.46061
Baum, Paul; Connes, Alain; Higson, Nigel
124
1994
Gravity and the standard model with neutrino mixing. Zbl 1140.81022
Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde
120
2007
Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Zbl 0759.58047
Connes, Alain; Moscovici, Henri
119
1990
An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R. Zbl 0461.46043
Connes, A.
118
1981
Hopf algebras, cyclic cohomology and the transverse index theorem. Zbl 0940.58005
Connes, A.; Moscovici, H.
117
1998
Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Zbl 0842.46040
Bost, J.-B.; Connes, A.
111
1995
The flow of weights on factors of type III. Zbl 0408.46047
Connes, Alain; Takesaki, Masamichi
108
1977
Noncommutative manifolds, the instanton algebra and isospectral deformations. Zbl 0997.81045
Connes, Alain; Landi, Giovanni
107
2001
Non-commutative geometry and physics. Zbl 0933.46069
Connes, A.
105
1995
Outer conjugacy classes of automorphisms of factors. Zbl 0342.46052
Connes, Alain
105
1975
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
102
2001
The action functional in non-commutative geometry. Zbl 0658.53068
Connes, A.
102
1988
Compact metric spaces, Fredholm modules, and hyperfiniteness. Zbl 0718.46051
Connes, A.
100
1989
C* algèbres et géométrie différentielle. Zbl 0433.46057
Connes, Alain
99
1980
Cohomologie cyclique et foncteurs \(Ext^ n\). Zbl 0534.18009
Connes, Alain
95
1983
Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples. Zbl 1026.58005
Connes, Alain; Dubois-Violette, Michel
93
2002
Dynamical entropy of C *-algebras and von Neumann algebras. Zbl 0637.46073
Connes, A.; Narnhofer, H.; Thirring, W.
93
1987
Noncommutative geometry, quantum fields and motives. Zbl 1209.58007
Connes, Alain; Marcolli, Matilde
91
2008
A survey of foliations and operator algebras. Zbl 0531.57023
Connes, A.
87
1982
Almost periodic states and factors of type III\(_1\). Zbl 0302.46050
Connes, A.
87
1974
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015
Connes, Alain
85
1999
Noncommutative geometry, quantum fields and motives. Zbl 1159.58004
Connes, Alain; Marcolli, Matilde
83
2008
Property \(T\) for von Neumann algebras. Zbl 1190.46047
Connes, A.; Jones, V.
82
1985
Entropy for automorphisms of \(II_1\) von Neumann algebras. Zbl 0326.46032
Connes, Alain; Størmer, Erling
80
1975
On the spectral characterization of manifolds. Zbl 1287.58004
Connes, Alain
75
2013
On the spatial theory of von Neumann algebras. Zbl 0443.46042
Connes, A.
69
1980
Caractérisation des espaces vectoriels ordonnés sous jacents aux algèbres de Von Neumann. Zbl 0287.46078
Connes, Alain
67
1974
Particle models and noncommutative geometry. Zbl 0957.46516
Connes, Alain; Lott, John
65
1990
Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules. Zbl 0657.46049
Connes, A.
62
1988
Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Zbl 1020.46505
Chamseddine, Ali H.; Connes, Alain
60
1996
Deformations, asymptotic morphisms and bivariant \(K\)-theory. Zbl 0717.46062
Connes, Alain; Higson, Nigel
59
1990
Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Zbl 0821.46086
Connes, A.; Rovelli, C.
58
1994
Sur la théorie non commutative de l’intégration. Zbl 0412.46053
Connes, Alain
58
1979
Why the standard model. Zbl 1140.81021
Chamseddine, Ali H.; Connes, Alain
53
2008
Geometry from the spectral point of view. Zbl 1042.46515
Connes, Alain
52
1995
A factor of type \(II_ 1\) with countable fundamental group. Zbl 0455.46056
Connes, A.
50
1980
Periodic automorphisms of the hyperfinite factor of type \(II_1\). Zbl 0382.46027
Connes, A.
49
1977
On the cohomology of operator algebras. Zbl 0408.46042
Connes, A.
48
1978
Modular curvature for noncommutative two-tori. Zbl 1332.46070
Connes, Alain; Moscovici, Henri
47
2014
Property T and asymptotically invariant sequences. Zbl 0479.28017
Connes, A.; Weiss, B.
47
1980
Type III and spectral triples. Zbl 1159.46041
Connes, Alain; Moscovici, Henri
46
2008
Yang-Mills for non-commutative two-tori. Zbl 0633.46069
Connes, Alain; Rieffel, Marc A.
46
1987
Homogeneity of the state space of factors of type \(III_1\). Zbl 0408.46048
Connes, Alain; Størmer, Erling
45
1978
The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037
Connes, Alain; Tretkoff, Paula
43
2011
Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012
Connes, Alain
43
2004
Introduction to non commutative differential geometry. Zbl 0564.58002
Connes, A.
42
1985
Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001
Connes, Alain; Consani, Caterina
41
2010
Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042
Baum, Paul; Connes, Alain
41
2000
The \(L^2\)-index theorem for homogeneous spaces of Lie groups. Zbl 0515.58031
Connes, Alain; Moscovici, Henri
39
1982
Cyclic cohomology and the transverse fundamental class of a foliation. Zbl 0647.46054
Connes, A.
37
1986
A short survey of noncommutative geometry. Zbl 0974.58008
Connes, Alain
36
2000
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 factor not anti-isomorphic to itself. Zbl 0315.46058
Connes, A.
35
1975
Noncommutative geometry. Zbl 0745.46067
Connes, Alain
34
1990
Chern character for discrete groups. Zbl 0656.55005
Baum, Paul; Connes, Alain
32
1988
A \(\text{II}_1\) factor with two nonconjugate Cartan subalgebras. Zbl 0501.46056
Connes, A.; Jones, V.
32
1982
Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Zbl 1122.11024
Connes, Alain; Moscovici, Henri
31
2004
The hyperring of adèle classes. Zbl 1221.14002
Connes, Alain; Consani, Caterina
30
2011
Yang-Mills algebra. Zbl 1028.53025
Connes, Alain; Dubois-Violette, Michel
29
2002
Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. Zbl 0369.28013
Connes, Alain; Krieger, Wolfgang
29
1977
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 physics to number theory via noncommutative geometry. Zbl 1126.58006
Connes, Alain; Marcolli, Matilde
26
2006
Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity). Zbl 0664.46067
Connes, A.; Cuntz, J.
26
1988
Characteristic 1, entropy and the absolute point. Zbl 1273.11140
Connes, Alain; Consani, Caterina
25
2011
A walk in the noncommutative garden. Zbl 1145.14005
Connes, Alain; Marcolli, Matilde
25
2008
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013
Connes, Alain; Moscovici, Henri
25
2001
Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
24
2013
Resilience of the spectral standard model. Zbl 1397.81412
Chamseddine, Ali H.; Connes, Alain
24
2012
Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190
Chamseddine, Ali H.; Connes, Alain
24
2007
Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006
Connes, Alain; Moscovici, Henri
24
2000
Approximately transitive flows and ITPFI factors. Zbl 0606.46041
Connes, A.; Woods, E. J.
24
1985
Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001
Connes, Alain; Consani, Caterina; Marcolli, Matilde
23
2007
Scale invariance in the spectral action. Zbl 1112.83036
Chamseddine, Ali H.; Connes, Alain
23
2006
KMS states and complex multiplication. Zbl 1106.58005
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
23
2005
\(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034
Connes, Alain; Shlyakhtenko, Dimitri
23
2005
Transgression and the Chern character of finite-dimensional K-cycles. Zbl 0793.58006
Connes, Alain; Moscovici, Henri
23
1993
On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006
Connes, Alain; Consani, Caterina
22
2011
The metric aspect of noncommutative geometry. Zbl 1221.58007
Connes, Alain; Lott, John
22
1992
Sur la classification des facteurs de type II. Zbl 0304.46042
Connes, Alain
22
1975
The arithmetic site. Zbl 1315.11054
Connes, Alain; Consani, Caterina
21
2014
Fun with \(\mathbb F_1\). Zbl 1228.11143
Connes, Alain; Consani, Caterina; Marcolli, Matilde
21
2009
Modular Hecke algebras and their Hopf symmetry. Zbl 1122.11023
Connes, Alain; Moscovici, Henri
21
2004
Group cohomology with Lipschitz control and higher signatures. Zbl 0789.58069
Connes, A.; Gromov, M.; Moscovici, H.
21
1993
Classification des facteurs. Zbl 0503.46043
Connes, A.
21
1982
Entropy and the spectral action. Zbl 1444.46049
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
2
2020
\(\overline{\operatorname{Spec}\mathbb{Z}}\) and the Gromov norm. Zbl 1444.16061
Connes, Alain; Consani, Caterina
1
2020
The term \(a_4\) in the heat kernel expansion of noncommutative tori. Zbl 1433.58008
Connes, Alain; Fathizadeh, Farzad
6
2019
Conformal trace theorem for Julia sets of quadratic polynomials. Zbl 1425.37032
Connes, A.; Mcdonald, E.; Sukochev, F.; Zanin, D.
6
2019
Homological algebra in characteristic one. Zbl 1411.18006
Connes, Alain; Consani, Caterina
5
2019
Noncommutative geometry for symmetric non-self-adjoint operators. Zbl 07063161
Connes, Alain; Levitina, Galina; McDonald, Edward; Sukochev, Fedor; Zanin, Dmitriy
2
2019
Geometry and the quantum. Zbl 1411.58003
Connes, Alain
1
2018
Geometry of the scaling site. Zbl 1406.11118
Connes, Alain; Consani, Caterina
7
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
15
2016
Absolute algebra and Segal’s \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\). Zbl 1409.14046
Connes, Alain; Consani, Caterina
7
2016
An essay on the Riemann hypothesis. Zbl 1353.11095
Connes, Alain
5
2016
The scaling site. Zbl 1348.18004
Connes, Alain; Consani, Caterina
5
2016
Grand unification in the spectral Pati-Salam model. Zbl 1388.81965
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
15
2015
Universal thickening of the field of real numbers. Zbl 1387.11086
Connes, Alain; Consani, Caterina
13
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
47
2014
The arithmetic site. Zbl 1315.11054
Connes, Alain; Consani, Caterina
21
2014
Geometry and the quantum: basics. Zbl 1333.81414
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
14
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
75
2013
Inner fluctuations in noncommutative geometry without the first order condition. Zbl 1284.58014
Chamseddine, Ali H.; Connes, Alain; Van Suijlekom, Walter D.
24
2013
Beyond the spectral standard model: emergence of Pati-Salam unification. Zbl 1410.81032
Chamseddine, Ali H.; Connes, Alain; van Suijlekom, Walter D.
17
2013
Resilience of the spectral standard model. Zbl 1397.81412
Chamseddine, Ali H.; Connes, Alain
24
2012
Spectral action for Robertson-Walker metrics. Zbl 1397.81413
Chamseddine, Ali H.; Connes, Alain
14
2012
The Gauss-Bonnet theorem for the noncommutative two torus. Zbl 1251.46037
Connes, Alain; Tretkoff, Paula
43
2011
The hyperring of adèle classes. Zbl 1221.14002
Connes, Alain; Consani, Caterina
30
2011
Characteristic 1, entropy and the absolute point. Zbl 1273.11140
Connes, Alain; Consani, Caterina
25
2011
On the notion of geometry over \(\mathbb{F}_{1}\). Zbl 1227.14006
Connes, Alain; Consani, Caterina
22
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
Connes, Alain (ed.); Gorokhovsky, Alexander (ed.); Lesch, Matthias (ed.); Pflaum, Markus (ed.); Rnagipour, Bahram (ed.)
1
2011
Schemes over \(\mathbb F_{1}\) and zeta functions. Zbl 1201.14001
Connes, Alain; Consani, Caterina
41
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
20
2010
The uncanny precision of the spectral action. Zbl 1192.58005
Chamseddine, Ali H.; Connes, Alain
17
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
Alon, Noga (ed.); Bourgain, Jean (ed.); Connes, Alain (ed.); Gromov, Mikhael (ed.); Milman, Vitali D. (ed.)
1
2010
Fun with \(\mathbb F_1\). Zbl 1228.11143
Connes, Alain; Consani, Caterina; Marcolli, Matilde
21
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
Connes, Alain (ed.); Fauvet, Frédéric (ed.); Ramis, Jean-Pierre (ed.)
1
2009
Noncommutative geometry, quantum fields and motives. Zbl 1209.58007
Connes, Alain; Marcolli, Matilde
91
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
53
2008
Type III and spectral triples. Zbl 1159.46041
Connes, Alain; Moscovici, Henri
46
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
120
2007
Conceptual explanation for the algebra in the noncommutative approach to the standard model. Zbl 1228.81190
Chamseddine, Ali H.; Connes, Alain
24
2007
Noncommutative geometry and motives: the thermodynamics of endomotives. Zbl 1125.14001
Connes, Alain; Consani, Caterina; Marcolli, Matilde
23
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
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
4
2007
Noncommutative geometry. Abstracts from the workshop held September 2–8, 2007. Zbl 1177.58003
Connes, Alain (ed.); Cuntz, Joachim (ed.); Rieffel, Marc A. (ed.)
2
2007
On the foundations of noncommutative geometry. Zbl 1106.58004
Connes, A.
221
2006
From physics to number theory via noncommutative geometry. Zbl 1126.58006
Connes, Alain; Marcolli, Matilde
26
2006
Scale invariance in the spectral action. Zbl 1112.83036
Chamseddine, Ali H.; Connes, Alain
23
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
6
2006
Transgressions of the Godbillon-Vey class and Rademacher functions. Zbl 1109.11027
Connes, Alain; Moscovici, Henri
1
2006
KMS states and complex multiplication. Zbl 1106.58005
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan
23
2005
\(L^2\)-cohomology for von Neumann algebras. Zbl 1083.46034
Connes, Alain; Shlyakhtenko, Dimitri
23
2005
Cyclic cohomology, quantum group symmetries and the local index formula for \(SU_q(2)\). Zbl 1074.58012
Connes, Alain
43
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
10
2004
Cyclic cohomology, noncommutative geometry and quantum group symmetries. Zbl 1052.46057
Connes, Alain
5
2004
Renormalization and Galois ambiguity. 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. 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
93
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
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
107
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
102
2001
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry. Zbl 1018.57013
Connes, Alain; Moscovici, Henri
25
2001
From local perturbation theory to Hopf- and Lie-algebras of Feynman graphs. Zbl 1015.81042
Connes, A.; Kreimer, D.
4
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 0995.81077
Connes, Alain; Kreimer, Dirk
4
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
192
2000
Geometric \(K\)-theory for Lie groups and foliations. Zbl 0985.46042
Baum, Paul; Connes, Alain
41
2000
A short survey of noncommutative geometry. Zbl 0974.58008
Connes, Alain
36
2000
Cyclic cohomology and Hopf algebra symmetry. Zbl 0974.58006
Connes, Alain; Moscovici, Henri
24
2000
Noncommutative geometry year 2000. Zbl 0985.58003
Connes, Alain
15
2000
Noncommutative geometry and the Riemann zeta function. Zbl 0960.11042
Connes, Alain
3
2000
Cyclic cohomology and Hopf algebra symmetry. Zbl 0970.58005
Connes, Alain; Moscovici, Henri
2
2000
GAFA 2000. Visions in mathematics—Towards 2000. Proceedings of a meeting, Tel Aviv, Israel, August 25–September 3, 1999. Part II. Special volume of the journal Geometric and Functional Analysis. Zbl 0960.00035
Alon, N. (ed.); Bourgain, Jean (ed.); Connes, A. (ed.); Gromov, M. (ed.); Milman, V. (ed.)
1
2000
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Zbl 0945.11015
Connes, Alain
85
1999
Cyclic cohomology and Hopf algebras. Zbl 0941.16024
Connes, Alain; Moscovici, Henri
36
1999
Renormalization in quantum field theory and the Riemann-Hilbert problem. Zbl 0957.81011
Connes, Alain; Kreimer, Dirk
11
1999
...and 123 more Documents
all top 5

Cited by 3,494 Authors

84 Connes, Alain
50 Marcolli, Matilde
49 Sukochev, Fedor Anatol’evich
44 Guo, Li
44 Popa, Sorin Teodor
36 van Suijlekom, Walter Daniël
31 Landi, Giovanni
31 Rennie, Adam
30 Sitarz, Andrzej
29 Iochum, Bruno
28 Carey, Alan L.
28 Khalkhali, Masoud
28 Longo, Roberto
27 Dabrowski, Ludwik
26 Majid, Shahn
26 Vaes, Stefaan
25 Houdayer, Cyril
25 Martinetti, Pierre
23 Haagerup, Uffe Valentin
23 Lizzi, Fedele
23 Ponge, Raphaël S.
23 Skandalis, Georges
22 Ebrahimi-Fard, Kurusch
22 Neshveyev, Sergey V.
22 Yu, Guoliang
21 Benameur, Moulay-Tahar
21 Chamseddine, Ali Hani
21 Consani, Caterina
21 Golodets, Valentin Yakovlevich
21 Ioana, Adrian
21 Wulkenhaar, Raimar
20 Goswami, Debashish
20 Laca, Marcelo
20 Mathai, Varghese
20 Zanin, Dmitriy V.
19 D’Andrea, Francesco
19 Dubois-Violette, Michel
19 Jørgensen, Palle E. T.
19 Narnhofer, Heide
19 Schücker, Thomas
18 Kaad, Jens
18 Nest, Ryszard
18 Wang, Yong
17 Bai, Chengming
17 Brzeziński, Tomasz
17 Moscovici, Henri
17 Rangipour, Bahram
17 Størmer, Erling
16 Cho, Ilwoo
16 Foissy, Loïc
16 Gao, Xing
16 Wallet, Jean-Christophe
15 Chakraborty, Partha Sarathi
15 Choda, Marie
15 Elliott, George A.
15 Manchon, Dominique
15 Takesaki, Masamichi
15 Thomsen, Klaus E.
14 Bhowmick, Jyotishman
14 Cuntz, Joachim
14 Fathizadeh, Farzad
14 Gracia-Bondía, José M.
14 Junge, Marius
14 Latrémolière, Frédéric
14 Lorscheid, Oliver
14 Nistor, Victor
14 Stephan, Christoph A.
14 Voiculescu, Dan-Virgil
13 Chifan, Ionuţ
13 Christensen, Erik
13 Dadarlat, Marius
13 Klimek, Slawomir
13 Lesniewski, Andrzej
13 Patras, Frédéric
13 Paycha, Sylvie
13 Schulz-Baldes, Hermann
13 Tang, Xiang
13 Tomatsu, Reiji
13 Várilly, Joseph C.
12 Bellissard, Jean V.
12 Fidaleo, Francesco
12 Gayral, Victor
12 Grosse, Harald
12 Iovane, Gerardo
12 Jones, Vaughan Frederick Randal
12 Kishimoto, Akitaka
12 Masson, Thierry
12 Masuda, Toshihiko
12 Meyer, Ralf
12 Schrohe, Elmar
12 Shlyakhtenko, Dimitri L.
11 Aastrup, Johannes
11 Bieliavsky, Pierre
11 Giordano, Thierry
11 Heller, Michał P.
11 Hiai, Fumio
11 Kastler, Daniel
11 Kellendonk, Johannes
11 Larsen, Nadia S.
11 Lesch, Matthias
...and 3,394 more Authors
all top 5

Cited in 365 Serials

399 Journal of Functional Analysis
313 Communications in Mathematical Physics
238 Journal of Geometry and Physics
183 Advances in Mathematics
181 Journal of Mathematical Physics
148 Letters in Mathematical Physics
146 Journal of Noncommutative Geometry
139 Nuclear Physics. B
106 Proceedings of the American Mathematical Society
97 Transactions of the American Mathematical Society
92 Journal of High Energy Physics
75 \(K\)-Theory
69 Journal of Algebra
68 Journal of Pure and Applied Algebra
62 Mathematische Annalen
61 Ergodic Theory and Dynamical Systems
60 Publications of the Research Institute for Mathematical Sciences, Kyoto University
57 Inventiones Mathematicae
55 Comptes Rendus. Mathématique. Académie des Sciences, Paris
53 International Journal of Mathematics
51 Journal of Mathematical Analysis and Applications
50 Physics Letters. B
48 International Journal of Modern Physics A
47 International Journal of Geometric Methods in Modern Physics
45 International Journal of Theoretical Physics
45 Reviews in Mathematical Physics
40 Chaos, Solitons and Fractals
38 Journal für die Reine und Angewandte Mathematik
35 Israel Journal of Mathematics
32 Journal of \(K\)-Theory
28 Communications in Algebra
27 Bulletin of the American Mathematical Society. New Series
26 Annales de l’Institut Fourier
24 Reports on Mathematical Physics
24 Journal of Number Theory
24 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
23 Annales Henri Poincaré
22 General Relativity and Gravitation
22 Acta Mathematica
22 Integral Equations and Operator Theory
21 Rocky Mountain Journal of Mathematics
20 Modern Physics Letters A
20 Duke Mathematical Journal
20 Geometric and Functional Analysis. GAFA
20 Journal of Mathematical Sciences (New York)
18 Mathematische Zeitschrift
18 Russian Journal of Mathematical Physics
18 Mathematical Physics, Analysis and Geometry
18 Science China. Mathematics
16 Acta Mathematica Sinica. English Series
16 Journal of Algebra and its Applications
16 Groups, Geometry, and Dynamics
15 Expositiones Mathematicae
15 Infinite Dimensional Analysis, Quantum Probability and Related Topics
14 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
14 Tohoku Mathematical Journal. Second Series
14 Topology and its Applications
14 Nuclear Physics, B, Proceedings Supplements
14 Bulletin des Sciences Mathématiques
14 Complex Analysis and Operator Theory
13 Journal d’Analyse Mathématique
13 Memoirs of the American Mathematical Society
13 Annals of Physics
13 Applied Categorical Structures
13 Advances in Applied Clifford Algebras
12 Compositio Mathematica
12 Functional Analysis and its Applications
12 Proceedings of the Japan Academy. Series A
12 Acta Applicandae Mathematicae
12 Journal of the American Mathematical Society
12 Journal of Algebraic Combinatorics
12 Foundations of Physics
12 Journal of Pseudo-Differential Operators and Applications
11 Mathematical Notes
11 Mathematical Proceedings of the Cambridge Philosophical Society
11 Physics Letters. A
11 Bulletin de la Société Mathématique de France
11 Journal of Soviet Mathematics
11 Linear Algebra and its Applications
11 Selecta Mathematica. New Series
11 Documenta Mathematica
11 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics
10 Publications Mathématiques
10 Journal of the Australian Mathematical Society
10 Journal of Topology and Analysis
10 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
9 Bulletin of the Australian Mathematical Society
9 Manuscripta Mathematica
9 Annales de l’Institut Henri Poincaré. Physique Théorique
9 Annales Mathématiques Blaise Pascal
9 Geometry & Topology
9 Algebras and Representation Theory
9 Physical Review Letters
9 Journal of Homotopy and Related Structures
8 Geometriae Dedicata
8 Differential Geometry and its Applications
8 Proceedings of the National Academy of Sciences of the United States of America
8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
8 Annals of Mathematics. Second Series
8 Banach Journal of Mathematical Analysis
...and 265 more Serials
all top 5

Cited in 61 Fields

2,219 Functional analysis (46-XX)
1,315 Quantum theory (81-XX)
966 Global analysis, analysis on manifolds (58-XX)
567 Associative rings and algebras (16-XX)
454 \(K\)-theory (19-XX)
401 Operator theory (47-XX)
387 Topological groups, Lie groups (22-XX)
376 Differential geometry (53-XX)
346 Nonassociative rings and algebras (17-XX)
327 Relativity and gravitational theory (83-XX)
318 Dynamical systems and ergodic theory (37-XX)
278 Group theory and generalizations (20-XX)
256 Category theory; homological algebra (18-XX)
240 Number theory (11-XX)
198 Algebraic geometry (14-XX)
196 Manifolds and cell complexes (57-XX)
166 Measure and integration (28-XX)
165 Combinatorics (05-XX)
161 Algebraic topology (55-XX)
149 Statistical mechanics, structure of matter (82-XX)
121 Abstract harmonic analysis (43-XX)
95 Probability theory and stochastic processes (60-XX)
91 Partial differential equations (35-XX)
62 Commutative algebra (13-XX)
58 Mathematical logic and foundations (03-XX)
55 Several complex variables and analytic spaces (32-XX)
53 Linear and multilinear algebra; matrix theory (15-XX)
52 General topology (54-XX)
48 Order, lattices, ordered algebraic structures (06-XX)
43 Information and communication theory, circuits (94-XX)
38 Ordinary differential equations (34-XX)
37 Field theory and polynomials (12-XX)
32 Convex and discrete geometry (52-XX)
31 Functions of a complex variable (30-XX)
31 Computer science (68-XX)
29 Mechanics of particles and systems (70-XX)
28 Harmonic analysis on Euclidean spaces (42-XX)
25 Geometry (51-XX)
24 General and overarching topics; collections (00-XX)
19 Special functions (33-XX)
17 Numerical analysis (65-XX)
16 General algebraic systems (08-XX)
14 History and biography (01-XX)
10 Real functions (26-XX)
10 Statistics (62-XX)
10 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
9 Optics, electromagnetic theory (78-XX)
9 Classical thermodynamics, heat transfer (80-XX)
9 Astronomy and astrophysics (85-XX)
9 Operations research, mathematical programming (90-XX)
7 Difference and functional equations (39-XX)
6 Potential theory (31-XX)
6 Sequences, series, summability (40-XX)
6 Approximations and expansions (41-XX)
6 Calculus of variations and optimal control; optimization (49-XX)
6 Systems theory; control (93-XX)
5 Integral transforms, operational calculus (44-XX)
3 Integral equations (45-XX)
2 Fluid mechanics (76-XX)
2 Biology and other natural sciences (92-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.