Publications

278.

Noncommutativity and physics: a non-technical review

Ali Chamseddine, Alain Connes, Walter van Suijlekom

Eur. Phys. J. Spec. Top., vol. 232, p. 3581–3588, 2023.

Résumé

277.

Riemann-Roch for Spec Z

Alain Connes, Caterina Consani

Bull. Sci. Math. , vol. 187, 2023.

Résumé

276.

Hochschild homology, trace map and zeta-cycles

Alain Connes, Caterina Consani

Proc. Sympos. Pure Math , vol. 105, p. 83–101, 2023.

Résumé

275.

Cyclic theory and the pericyclic category

Alain Connes, Caterina Consani

Proc. Sympos. Pure Math, vol. 105, p. 103–122, 2023.

Résumé

274.

Spectral triples and zeta cycles

Alain Connes, Caterina Consani

Enseign. Math., vol. 69, no. 1--2, p. 93–148, 2023.

Résumé

273.

BC-system, absolute cyclotomy and the quantized calculus

Alain Connes, Caterina Consani

EMS Surv. Math. Sci. , vol. 9, no. 2, p. 447–475, 2022.

Résumé

272.

The UV prolate spectrum matches the zeros of zeta

Alain Connes, Henri Moscovici

Proc. Natl. Acad. Sci. USA, vol. 119, iss. 119, no. 22, p. 7 pages, 2022.

Résumé

271.

Prolate spheroidal operator and ZetaÀ paraître

Alain Connes, Henri Moscovici

À paraître.

Résumé

270.

Tolerance relations and operator systemsÀ paraître

Alain Connes, Walter D. van Suijlekom

À paraître.

Résumé

269.

Spectral Triples and Zeta-CyclesÀ paraître

Alain Connes, Caterina Consani

Enseignement Mathématique, À paraître.

Résumé

268.

Quasi-inner functions and local factors

Alain Connes, Caterina Consani

Journal of Number Theory, vol. 226, p. 139-167, 2021.

Résumé

267.

On absolute algebraic geometry, the affine case

Alain Connes, Caterina Consani

Advances in Mathematics, vol. 390, p. 1–45, 2021.

Résumé

266.

Weil positivity and trace formula, the archimedean place

Alain Connes, Caterina Consani

Selecta Mathematica, vol. 27, no. 4, 2021.

Résumé

265.

Noncommutative Geometry, the Spectral Standpoint

Alain Connes

Cambridge University Press (Ed.): Cambridge University Press, 2021.

Résumé

264.

Spectral truncation in noncommutative geometry and operator systems

Alain Connes, Walter D. van Suijlekom

Communication in Mathematical Physics, vol. 383, p. 2021–2067, 2021.

Résumé

263.

Segal's Gamma Rings and Universal Arithmetic

Alain Connes, Caterina Consani

Quarterly Journal of Mathematics, p. 1-29, 2020.

Résumé

262.

Motivic Rhythms

Alain Connes

Journal of Mathematics and Music, vol. 15, no. 1, p. 1–16, 2020, ISSN: 1745-9737.

Résumé

261.

The scaling Hamiltonian

Alain Connes, Caterina Consani

J. Operator Theory, vol. 85, no. 1, p. 257–276, 2019, ISSN: 0379-4024.

Résumé

260.

Sir Michael Atiyah, a Knight Mathematician

Alain Connes, Joseph Kouneiher

Notices Amer. Math. Soc., vol. 66, no. 10, p. 1660–1671, 2019, ISSN: 0002-9920.

Résumé

259.

La géométrie et le quantique

Alain Connes

CNRS Éditions, Paris, 2019, ISBN: 978-2-271-12712-9.

Résumé

258.

Sp̅e̅c̅ ℤ and the Gromov norm

Alain Connes, Caterina Consani

Theory Appl. Categ., vol. 35, no. 6, p. 155–178, 2019.

Résumé

257.

The term a₄ in the heat kernel expansion of noncommutative tori

Alain Connes, Farzad Fathizadeh

Münster J. Math., vol. 12, no. 2, p. 239–410, 2019, ISSN: 1867-5778.

Résumé

256.

Conformal trace theorem for Julia sets of quadratic polynomials

Alain Connes, Edward McDonald, Fedor A. Sukochev, Dimitriy V. Zanin

Ergodic Theory Dynam. Systems, vol. 39, no. 9, p. 2481–2506, 2019, ISSN: 0143-3857.

Résumé

255.

Noncommutative geometry for symmetric non-self-adjoint operators

Alain Connes, Galina Levitina, Edward McDonald, Fedor A. Sukochev, Dimitriy V. Zanin

J. Funct. Anal., vol. 277, no. 3, p. 889–936, 2019, ISSN: 0022-1236.

Résumé

254.

Homological algebra in characteristic one

Alain Connes, Caterina Consani

High. Struct., vol. 3, no. 1, p. 155–247, 2019.

Résumé

253.

Iteration of the exterior power on representation rings

Alain Connes

J. Geom. Phys., vol. 141, p. 1–10, 2019, ISSN: 0393-0440.

Résumé

252.

Around Wilson's theorem

Alain Connes

J. Number Theory, vol. 194, p. 1–7, 2018, ISSN: 0022-314X.

Résumé

251.

Entropy and the spectral action

Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom

Comm. Math. Phys., vol. 373, no. 2, p. 457–471, 2018, ISSN: 0010-3616.

Résumé

250.

Le Spectre d'Atacama

Alain Connes, Danye Chéreau, Jacques Dixmier

2018, ISBN: 9782738141361.

Résumé

249.

Geometry and the quantum

Alain Connes

Foundations of mathematics and physics one century after Ħilbert, p. 159–196, Springer, Cham, 2018.

Résumé

248.

Trace theorem for quasi-Fuchsian groups

Alain Connes, Fedor A. Sukochev, Dimitriy V. Zanin

Mat. Sb., vol. 208, no. 10, p. 59–90, 2017, ISSN: 0368-8666.

Résumé

247.

Geometry of the scaling site

Alain Connes, Caterina Consani

Selecta Math. (N.S.), vol. 23, no. 3, p. 1803–1850, 2017, ISSN: 1022-1824.

Résumé

246.

An essay on the Riemann hypothesis

Alain Connes

Open problems in mathematics, p. 225–257, Springer, [Cham], 2016.

Résumé

245.

Geometry of the arithmetic site

Alain Connes, Caterina Consani

Adv. Math., vol. 291, p. 274–329, 2016, ISSN: 0001-8708.

Résumé

244.

Absolute algebra and Segal's Γ-rings

Alain Connes, Caterina Consani

J. Number Theory, vol. 162, p. 518–551, 2016, ISSN: 0022-314X.

Résumé

243.

The scaling site

Alain Connes, Caterina Consani

C. R. Math. Acad. Sci. Paris, vol. 354, no. 1, p. 1–6, 2016, ISSN: 1631-073X.

Résumé

242.

Uffe Haagerup—In memoriam

Alain Connes, Vaughan Jones, Magdalena Musat, Mikael Rørdam

Notices Amer. Math. Soc., vol. 63, no. 1, p. 48–49, 2016, ISSN: 0002-9920.

Résumé

241.

Grand unification in the spectral Pati–Salam model

Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom

J. High Energy Phys., no. 11, p. 011, front matter+12, 2015, ISSN: 1126-6708.

Résumé

240.

Quanta of geometry: noncommutative aspects

Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov

Phys. Rev. Lett., vol. 114, no. 9, p. 091302, 5, 2015, ISSN: 0031-9007.

Résumé

239.

The cyclic and epicyclic sites

Alain Connes, Caterina Consani

Rend. Semin. Mat. Univ. Padova, vol. 134, p. 197–237, 2015, ISSN: 0041-8994.

Résumé

238.

Universal thickening of the field of real numbers

Alain Connes, Caterina Consani

Advances in the theory of numbers, vol. 77, p. 11–74, Fields Inst. Res. Math. Sci., Toronto, ON, 2015.

Résumé

237.

Projective geometry in characteristic one and the epicyclic category

Alain Connes, Caterina Consani

Nagoya Math. J., vol. 217, p. 95–132, 2015, ISSN: 0027-7630.

Résumé

236.

Cyclic structures and the topos of simplicial sets

Alain Connes, Caterina Consani

J. Pure Appl. Algebra, vol. 219, no. 4, p. 1211–1235, 2015, ISSN: 0022-4049.

Résumé

235.

Geometry and the quantum: basics

Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov

J. High Energy Phys., no. 12, p. 098, front matter+24, 2014, ISSN: 1126-6708.

Résumé

234.

The arithmetic site

Alain Connes, Caterina Consani

C. R. Math. Acad. Sci. Paris, vol. 352, no. 12, p. 971–975, 2014, ISSN: 1631-073X.

Résumé

233.

On the arithmetic of the BC-system

Alain Connes, Caterina Consani

J. Noncommut. Geom., vol. 8, no. 3, p. 873–945, 2014, ISSN: 1661-6952.

Résumé

232.

Cyclic homology, Serre's local factors and λ-operations

Alain Connes, Caterina Consani

J. K-Theory, vol. 14, no. 1, p. 1–45, 2014, ISSN: 1865-2433.

Résumé

231.

Modular curvature for noncommutative two-tori

Alain Connes, Henri Moscovici

J. Amer. Math. Soc., vol. 27, no. 3, p. 639–684, 2014, ISSN: 0894-0347.

Résumé

230.

Le théâtre quantique

Alain Connes, Danye Chéreau, Jacques Dixmier

2013, ISBN: 9782738129833.

Résumé

229.

Inner fluctuations in noncommutative geometry without the first order condition

Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom

J. Geom. Phys., vol. 73, p. 222–234, 2013, ISSN: 0393-0440.

Résumé

228.

On the spectral characterization of manifolds

Alain Connes

J. Noncommut. Geom., vol. 7, no. 1, p. 1–82, 2013, ISSN: 1661-6952.

Résumé

227.

Resilience of the spectral standard model

Ali H. Chamseddine, Alain Connes

J. High Energy Phys., no. 9, p. 104, front matter+10, 2012, ISSN: 1126-6708.

Résumé

226.

Spectral action for Robertson-Walker metrics

Ali H. Chamseddine, Alain Connes

J. High Energy Phys., no. 10, p. 101, front matter + 29, 2012, ISSN: 1126-6708.

Résumé

225.

The Gauss-Bonnet theorem for the noncommutative two torus

Alain Connes, Paula Tretkoff

Noncommutative geometry, arithmetic, and related topics, p. 141–158, Johns Hopkins Univ. Press, Baltimore, MD, 2011.

Résumé

224.

Characteristic 1, entropy and the absolute point

Alain Connes, Caterina Consani

Noncommutative geometry, arithmetic, and related topics, p. 75–139, Johns Hopkins Univ. Press, Baltimore, MD, 2011.

Résumé

223.

The BC-system and ?-functions

Alain Connes

Jpn. J. Math., vol. 6, no. 1, p. 1–44, 2011, ISSN: 0289-2316.

Résumé

222.

The Witt construction in characteristic one and quantization

Alain Connes

Noncommutative geometry and global analysis, vol. 546, p. 83–113, Amer. Math. Soc., Providence, RI, 2011.

Résumé

221.

On the notion of geometry over ?₁

Alain Connes, Caterina Consani

J. Algebraic Geom., vol. 20, no. 3, p. 525–557, 2011, ISSN: 1056-3911.

Résumé

220.

L'hyperanneau des classes d'adèles

Alain Connes

J. Théor. Nombres Bordeaux, vol. 23, no. 1, p. 71–93, 2011, ISSN: 1246-7405.

Résumé

219.

Noncommutative geometric spaces with boundary: spectral action

Ali H. Chamseddine, Alain Connes

J. Geom. Phys., vol. 61, no. 1, p. 317–332, 2011, ISSN: 0393-0440.

Résumé

218.

The hyperring of adèle classes

Alain Connes, Caterina Consani

J. Number Theory, vol. 131, no. 2, p. 159–194, 2011, ISSN: 0022-314X.

Résumé

217.

From monoids to hyperstructures: in search of an absolute arithmetic

Alain Connes, Caterina Consani

Casimir force, Casimir operators and the Riemann hypothesis, p. 147–198, Walter de Gruyter, Berlin, 2010.

Résumé

216.

Schemes over ?₁ and zeta functions

Alain Connes, Caterina Consani

Compos. Math., vol. 146, no. 6, p. 1383–1415, 2010, ISSN: 0010-437X.

Résumé

215.

The end of an era

Alain Connes, Cédric Villani, Daniel Stroock

J. Funct. Anal., vol. 259, no. 11, p. 2759, 2010, ISSN: 0022-1236.

Résumé

214.

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I

Ali H. Chamseddine, Alain Connes

Fortschr. Phys., vol. 58, no. 6, p. 553–600, 2010, ISSN: 0015-8208.

Résumé

213.

The uncanny precision of the spectral action

Ali H. Chamseddine, Alain Connes

Comm. Math. Phys., vol. 293, no. 3, p. 867–897, 2010, ISSN: 0010-3616.

Résumé

212.

The Weil proof and the geometry of the adèles class space

Alain Connes, Caterina Consani, Matilde Marcolli

Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, vol. 269, p. 339–405, Birkhäuser Boston, Boston, MA, 2009.

Résumé

211.

Fun with ?₁

Alain Connes, Caterina Consani, Matilde Marcolli

J. Number Theory, vol. 129, no. 6, p. 1532–1561, 2009, ISSN: 0022-314X.

Résumé

210.

On space and time

Alain Connes, Michael Heller, Shahn Majid, Roger Penrose, John Polkinghorne, Andrew Taylor

Cambridge University Press, Cambridge, 2008, ISBN: 978-0-521-88926-1.

Résumé

209.

A unitary invariant in Riemannian geometry

Alain Connes

Int. J. Geom. Methods Mod. Phys., vol. 5, no. 8, p. 1215–1242, 2008, ISSN: 0219-8878.

Résumé

208.

On the fine structure of spacetime

Alain Connes

On space and time, p. 196–237, Cambridge Univ. Press, Cambridge, 2008.

207.

Type III and spectral triples

Alain Connes, Henri Moscovici

Traces in number theory, geometry and quantum fields, p. 57–71, Friedr. Vieweg, Wiesbaden, 2008.

Résumé

206.

A walk in the noncommutative garden

Alain Connes, Matilde Marcolli

An invitation to noncommutative geometry, p. 1–128, World Sci. Publ., Hackensack, NJ, 2008.

Résumé

205.

Noncommutative finite dimensional manifolds II: Moduli space and structure of noncommutative 3-spheres

Alain Connes, Michel Dubois-Violette

Comm. Math. Phys., vol. 281, no. 1, p. 23–127, 2008, ISSN: 0010-3616.

Résumé

204.

Why the standard model

Ali H. Chamseddine, Alain Connes

J. Geom. Phys., vol. 58, no. 1, p. 38–47, 2008, ISSN: 0393-0440.

Résumé

203.

Noncommutative geometry, quantum fields and motives

Alain Connes, Matilde Marcolli

American Mathematical Society, Providence, RI; Hindustan Book Agency, New Delhi, 2007, ISBN: 978-0-8218-4210-2.

Résumé

202.

Non-commutative geometry and the spectral model of space-time

Alain Connes

Quantum spaces, vol. 53, p. 203–227, Birkhäuser, Basel, 2007.

Résumé

201.

Gravity and the standard model with neutrino mixing

Ali H. Chamseddine, Alain Connes, Matilde Marcolli

Adv. Theor. Math. Phys., vol. 11, no. 6, p. 991–1089, 2007, ISSN: 1095-0761.

Résumé

200.

A property of parallelograms inscribed in ellipses

Alain Connes, Don Zagier

Amer. Math. Monthly, vol. 114, no. 10, p. 909–914, 2007, ISSN: 0002-9890.

Résumé

199.

Conceptual explanation for the algebra in the noncommutative approach to the standard model

Ali H. Chamseddine, Alain Connes

Phys. Rev. Lett., vol. 99, no. 19, p. 191601, 4, 2007, ISSN: 0031-9007.

Résumé

198.

Noncommutative geometry and motives: the thermodynamics of endomotives

Alain Connes, Caterina Consani, Matilde Marcolli

Adv. Math., vol. 214, no. 2, p. 761–831, 2007, ISSN: 0001-8708.

Résumé

197.

Quantum gravity boundary terms from the spectral action of noncommutative space

Ali H. Chamseddine, Alain Connes

Phys. Rev. Lett., vol. 99, no. 7, p. 071302, 4, 2007, ISSN: 0031-9007.

Résumé

196.

Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory

Alain Connes, Matilde Marcolli

Frontiers in number theory, physics, and geometry. II, p. 617–713, Springer, Berlin, 2007.

Résumé

195.

Yang-Mills and some related algebras

Alain Connes, Michel Dubois-Violette

Rigorous quantum field theory, vol. 251, p. 65–78, Birkhäuser, Basel, 2007.

Résumé

194.

Transgressions of the Godbillon-Vey class and Rademacher functions

Alain Connes, Henri Moscovici

Noncommutative geometry and number theory, p. 79–107, Friedr. Vieweg, Wiesbaden, 2006.

Résumé

193.

Morse inequalities for foliations

Alain Connes, Thierry Fack

?*-algebras and elliptic theory, p. 61–72, Birkhäuser, Basel, 2006.

192.

Noncommutative geometry and the standard model with neutrino mixing

Alain Connes

J. High Energy Phys., no. 11, p. 081, 19, 2006, ISSN: 1126-6708.

Résumé

191.

Inner fluctuations of the spectral action

Alain Connes, Ali H. Chamseddine

J. Geom. Phys., vol. 57, no. 1, p. 1–21, 2006, ISSN: 0393-0440.

Résumé

190.

KMS states and complex multiplication (Part II)

Alain Connes, Matilde Marcolli, Niranjan Ramachandran

Operator Algebras: Ŧhe Abel Symposium 2004, vol. 1, p. 15–59, Springer, Berlin, 2006.

Résumé

189.

From physics to number theory via noncommutative geometry

Alain Connes, Matilde Marcolli

Frontiers in number theory, physics, and geometry. I, p. 269–347, Springer, Berlin, 2006.

Résumé

188.

Scale invariance in the spectral action

Ali H. Chamseddine, Alain Connes

J. Math. Phys., vol. 47, no. 6, p. 063504, 19, 2006, ISSN: 0022-2488.

Résumé

187.

On the foundations of noncommutative geometry

Alain Connes

The unity of mathematics, vol. 244, p. 173–204, Birkhäuser Boston, Boston, MA, 2006.

186.

Quantum fields and motives

Alain Connes, Matilde Marcolli

J. Geom. Phys., vol. 56, no. 1, p. 55–85, 2006, ISSN: 0393-0440.

Résumé

185.

ℚ-lattices: quantum statistical mechanics and Galois theory

Alain Connes, Matilde Marcolli

J. Geom. Phys., vol. 56, no. 1, p. 2–23, 2006, ISSN: 0393-0440.

Résumé

184.

KMS states and complex multiplication

Alain Connes, Matilde Marcolli, Niranjan Ramachandran

Selecta Math. (N.S.), vol. 11, no. 3-4, p. 325–347, 2005, ISSN: 1022-1824.

Résumé

183.

?²-homology for von Neumann algebras

Alain Connes, Dimitri Shlyakhtenko

J. Reine Angew. Math., vol. 586, p. 125–168, 2005, ISSN: 0075-4102.

Résumé

182.

Symmetries

Alain Connes

Butl. Soc. Catalana Mat., vol. 19, no. 2, p. 7–23 (2005), 2004, ISSN: 0214-316X.

Résumé

181.

Renormalisation et ambiguïté galoisienne

Alain Connes

Asterisque, no. 296, p. 113–143, 2004, ISSN: 0303-1179, (Analyse complexe, syst`emes dynamiques, sommabilité des séries divergentes et théories galoisiennes. I).

Résumé

180.

Nombres de Betti ?² et facteurs de type II₁ (d'après D. Gaboriau et S. Popa)

Alain Connes

Astérisque, no. 294, p. ix, 321–333, 2004, ISSN: 0303-1179.

Résumé

179.

Renormalization and motivic Galois theory

Alain Connes, Matilde Marcolli

Int. Math. Res. Not., no. 76, p. 4073–4091, 2004, ISSN: 1073-7928.

178.

Rankin-Cohen brackets and the Hopf algebra of transverse geometry

Alain Connes, Henri Moscovici

Mosc. Math. J., vol. 4, no. 1, p. 111–130, 311, 2004, ISSN: 1609-3321.

Résumé

177.

Modular Hecke algebras and their Hopf symmetry

Alain Connes, Henri Moscovici

Mosc. Math. J., vol. 4, no. 1, p. 67–109, 310, 2004, ISSN: 1609-3321.

Résumé

176.

Noncommutative geometry

Alain Connes, Joachim Cuntz, Eric Guentner, Nigel Higson, Jerry Kaminker, John Roberts

Springer-Verlag, Berlin; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 2004, ISBN: 3-540-20357-5.

Résumé

175.

Cyclic cohomology, noncommutative geometry and quantum group symmetries

Alain Connes

Noncommutative geometry, vol. 1831, p. 1–71, Springer, Berlin, 2004.

174.

Cyclic cohomology, quantum group symmetries and the local index formula for ???(2)

Alain Connes

J. Inst. Math. Jussieu, vol. 3, no. 1, p. 17–68, 2004, ISSN: 1474-7480.

Résumé

173.

Symétries galoisiennes et renormalisation

Alain Connes

Poincaré Seminar 2002, vol. 30, p. 241–264, Birkhäuser, Basel, 2003.

Résumé

172.

Moduli space and structure of noncommutative 3-spheres

Alain Connes, Michel Dubois-Violette

Lett. Math. Phys., vol. 66, no. 1-2, p. 91–121, 2003, ISSN: 0377-9017.

Résumé

171.

Hommage à Laurent Schwartz

Alain Connes

Gaz. Math., no. 94, p. 7–8, 2002, ISSN: 0224-8999.

170.

Noncommutative geometry year 2000

Alain Connes

Highlights of mathematical physics (London, 2000), p. 49–110, Amer. Math. Soc., Providence, RI, 2002.

169.

Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples

Alain Connes, Michel Dubois-Violette

Comm. Math. Phys., vol. 230, no. 3, p. 539–579, 2002, ISSN: 0010-3616.

Résumé

168.

Yang-Mills algebra

Alain Connes, Michel Dubois-Violette

Lett. Math. Phys., vol. 61, no. 2, p. 149–158, 2002, ISSN: 0377-9017.

Résumé

167.

Insertion and elimination: the doubly infinite Lie algebra of Feynman graphs

Alain Connes, Dirk Kreimer

Ann. Henri Poincaré, vol. 3, no. 3, p. 411–433, 2002, ISSN: 1424-0637.

Résumé

166.

Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry

Alain Connes, Henri Moscovici

Essays on geometry and related topics, Vol. 1, 2, vol. 38, p. 217–255, Enseignement Math., Geneva, 2001.

Résumé

165.

From local perturbation theory to Hopf and Lie algebras of Feynman graphs

Alain Connes, Dirk Kreimer

Mathematical physics in mathematics and physics (Siena, 2000), vol. 30, p. 105–114, Amer. Math. Soc., Providence, RI, 2001.

164.

Triangle of thoughts

Alain Connes, André Lichnerowicz, Marcel Paul Schützenberger

American Mathematical Society, Providence, RI, 2001, ISBN: 0-8218-2614-X.

Résumé

163.

From local perturbation theory to Hopf and Lie algebras of Feynman graphs

Alain Connes, Dirk Kreimer

vol. 56, no. 1, p. 3–15, 2001, ISSN: 0377-9017, (EuroConférence Moshé Flato 2000, Part I (Dijon)).

162.

Noncommutative manifolds, the instanton algebra and isospectral deformations

Alain Connes, Giovanni Landi

Comm. Math. Phys., vol. 221, no. 1, p. 141–159, 2001, ISSN: 0010-3616.

Résumé

161.

Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The ?-function, diffeomorphisms and the renormalization group

Alain Connes, Dirk Kreimer

Comm. Math. Phys., vol. 216, no. 1, p. 215–241, 2001, ISSN: 0010-3616.

160.

Triangle de pensées

Alain Connes, André Lichnerowicz, Marcel Paul Schützenberger

Odile Jacob, Paris, 2000, ISBN: 9780821826140.

Résumé

159.

A lecture on noncommutative geometry

Alain Connes

no. Special Issue, p. 31–64, 2000, ISSN: 1120-6330, (Mathematics towards the third millennium (Rome, 1999)).

158.

Noncommutative geometry year 2000

Alain Connes

no. Special Volume, Part II, p. 481–559, 2000, ISSN: 1016-443X, (GAFA 2000 (Tel Aviv, 1999)).

Résumé

157.

Cyclic cohomology and Hopf algebra symmetry

Alain Connes, Henri Moscovici

Conférence Moshé Flato 1999, Vol. I (Dijon), vol. 21, p. 121–147, Kluwer Acad. Publ., Dordrecht, 2000.

156.

Geometric ?-theory for Lie groups and foliations

Paul Baum, Alain Connes

Enseign. Math. (2), vol. 46, no. 1-2, p. 3–42, 2000, ISSN: 0013-8584.

155.

A short survey of noncommutative geometry

Alain Connes

J. Math. Phys., vol. 41, no. 6, p. 3832–3866, 2000, ISSN: 0022-2488.

154.

Noncommutative geometry and the Riemann zeta function

Alain Connes

Mathematics: frontiers and perspectives, p. 35–54, Amer. Math. Soc., Providence, RI, 2000.

153.

Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem

Alain Connes, Dirk Kreimer

Comm. Math. Phys., vol. 210, no. 1, p. 249–273, 2000, ISSN: 0010-3616.

Résumé

152.

Hopf algebras, renormalization and noncommutative geometry

Alain Connes, Dirk Kreimer

Quantum field theory: perspective and prospective (Les Houches, 1998), vol. 530, p. 59–108, Kluwer Acad. Publ., Dordrecht, 1999.

Résumé

151.

Renormalization in quantum field theory and the Riemann-Hilbert problem

Alain Connes, Dirk Kreimer

J. High Energy Phys., no. 9, p. Paper 24, 8, 1999, ISSN: 1126-6708.

150.

Cyclic cohomology and Hopf algebras

Alain Connes, Henri Moscovici

vol. 48, no. 1, p. 97–108, 1999, ISSN: 0377-9017, (Moshé Flato (1937--1998)).

149.

Lessons from quantum field theory: Hopf algebras and spacetime geometries

Alain Connes, Dirk Kreimer

vol. 48, no. 1, p. 85–96, 1999, ISSN: 0377-9017, (Moshé Flato (1937--1998)).

Résumé

148.

Hypoelliptic operators, Hopf algebras and cyclic cohomology

Alain Connes

Algebraic ?-theory and its applications (Trieste, 1997), p. 164–205, World Sci. Publ., River Edge, NJ, 1999.

147.

Trace formula on the adèle class space and Weil positivity

Alain Connes

Current developments in mathematics, 1997 (Cambridge, MA), p. 5–64, Int. Press, Boston, MA, 1999.

146.

Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

Alain Connes

Selecta Math. (N.S.), vol. 5, no. 1, p. 29–106, 1999, ISSN: 1022-1824.

Résumé

145.

A new proof of Morley's theorem

Alain Connes

Les relations entre les mathématiques et la physique théorique, p. 43–46, Inst. Hautes Études Sci., Bures-sur-Yvette, 1998.

Résumé

144.

Hopf algebras, renormalization and noncommutative geometry

Alain Connes, Dirk Kreimer

Comm. Math. Phys., vol. 199, no. 1, p. 203–242, 1998, ISSN: 0010-3616.

143.

Hopf algebras, cyclic cohomology and the transverse index theorem

Alain Connes, Henri Moscovici

Comm. Math. Phys., vol. 198, no. 1, p. 199–246, 1998, ISSN: 0010-3616.

142.

Noncommutative differential geometry and the structure of space-time

Alain Connes

The geometric universe (Oxford, 1996), p. 49–80, Oxford Univ. Press, Oxford, 1998.

141.

Noncommutative geometry: the spectral aspect

Alain Connes

Symétries quantiques (Les Ħouches, 1995), p. 643–686, North-Holland, Amsterdam, 1998.

140.

Noncommutative geometry and matrix theory: compactification on tori

Alain Connes, Michael R. Douglas, Albert Schwarz

J. High Energy Phys., no. 2, p. Paper 3, 35, 1998, ISSN: 1126-6708.

Résumé

139.

Brisure de symétrie spontanée et géométrie du point de vue spectral

Alain Connes

Fields Medallists' lectures, vol. 5, p. 340–371, World Sci. Publ., River Edge, NJ, 1997.

138.

Noncommutative differential geometry and the structure of space time

Alain Connes

Quantum fields and quantum space time (Cargèse, 1996), vol. 364, p. 45–72, Plenum, New York, 1997.

137.

Noncommutative differential geometry and the structure of space time

Alain Connes

Operator algebras and quantum field theory (Rome, 1996), p. 330–358, Int. Press, Cambridge, MA, 1997.

136.

Brisure de symétrie spontanée et géométrie du point de vue spectral

Alain Connes

J. Geom. Phys., vol. 23, no. 3-4, p. 206–234, 1997, ISSN: 0393-0440.

135.

Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

Alain Connes

Journées "Équations aux Dérivées Partielles" (Saint-Jean-de-Monts, 1997), p. Exp. No. IV, 28, École Polytech., Palaiseau, 1997.

Résumé

134.

Noncommutative differential geometry and the structure of space time

Alain Connes

Deformation theory and symplectic geometry (Ascona, 1996), vol. 20, p. 1–33, Kluwer Acad. Publ., Dordrecht, 1997.

133.

Noncommutative differential geometry and the structure of space time

Alain Connes

Cyclic cohomology and noncommutative geometry (Waterloo, ON, 1995), vol. 17, p. 17–42, Amer. Math. Soc., Providence, RI, 1997.

132.

Brisure de symétrie spontanée et géométrie du point de vue spectral

Alain Connes

no. 241, p. Exp. No. 816, 5, 313–349, 1997, ISSN: 0303-1179, (Séminaire Bourbaki, Vol. 1995/96).

Résumé

131.

The spectral action principle

Ali H. Chamseddine, Alain Connes

Comm. Math. Phys., vol. 186, no. 3, p. 731–750, 1997, ISSN: 0010-3616.

Résumé

130.

Aspherical gravitational monopoles

Alain Connes, Thibault Damour, Pierre Fayet

Nuclear Phys. B, vol. 490, no. 1-2, p. 391–431, 1997, ISSN: 0550-3213.

Résumé

129.

Matrix Vieta theorem revisited

Alain Connes, Albert Schwarz

Lett. Math. Phys., vol. 39, no. 4, p. 349–353, 1997, ISSN: 0377-9017.

Résumé

128.

Gravity coupled with matter and the foundation of non-commutative geometry

Alain Connes

Comm. Math. Phys., vol. 182, no. 1, p. 155–176, 1996, ISSN: 0010-3616.

Résumé

127.

Formule de trace en géométrie non-commutative et hypothèse de Riemann

Alain Connes

C. R. Acad. Sci. Paris Sér. I Math., vol. 323, no. 12, p. 1231–1236, 1996, ISSN: 0764-4442.

126.

Universal formula for noncommutative geometry actions: unification of gravity and the standard model

Ali H. Chamseddine, Alain Connes

Phys. Rev. Lett., vol. 77, no. 24, p. 4868–4871, 1996, ISSN: 0031-9007.

125.

Polarized modules and Fredholm modules

Jacek Brodzki, Alain Connes, David Ellwood

Mat. Fiz. Anal. Geom., vol. 2, no. 1, p. 15–24, 1995, ISSN: 1027-1767.

124.

Non-commutative geometry and physics

Alain Connes

Gravitation et quantifications (Les Ħouches, 1992), p. 805–950, North-Holland, Amsterdam, 1995.

123.

Round table: physics and mathematics

Joel Lebowitz, Michael Atiyah, Edouard Brézin, Alain Connes, Juerg Fröhlich, David Gross, Arthur Jaffe, Leo Kadanoff, David Ruelle

XIth International Congress of Mathematical Physics (Paris, 1994), p. 691–705, Int. Press, Cambridge, MA, 1995.

122.

Quantized calculus and applications

Alain Connes

XIth International Congress of Mathematical Physics (Paris, 1994), p. 15–36, Int. Press, Cambridge, MA, 1995.

121.

Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory

Jean-Benoît Bost, Alain Connes

Selecta Math. (N.S.), vol. 1, no. 3, p. 411–457, 1995, ISSN: 1022-1824.

Résumé

120.

Noncommutative geometry and reality

Alain Connes

J. Math. Phys., vol. 36, no. 11, p. 6194–6231, 1995, ISSN: 0022-2488.

Résumé

119.

Geometry from the spectral point of view

Alain Connes

Lett. Math. Phys., vol. 34, no. 3, p. 203–238, 1995, ISSN: 0377-9017.

118.

The local index formula in noncommutative geometry

Alain Connes, Henri Moscovici

Geom. Funct. Anal., vol. 5, no. 2, p. 174–243, 1995, ISSN: 1016-443X.

Résumé

117.

Conversations on mind, matter, and mathematics

Jean-Pierre Changeux, Alain Connes

Princeton University Press, Princeton, NJ, 1995, ISBN: 0-691-08759-8.

Résumé

116.

Noncommutative geometry

Alain Connes

Academic Press, Inc., San Diego, CA, 1994, ISBN: 0-12-185860-X.

Résumé

115.

Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories

Alain Connes, Carlo Rovelli

Classical Quantum Gravity, vol. 11, no. 12, p. 2899–2917, 1994, ISSN: 0264-9381.

Résumé

114.

Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes

Alain Connes, Dennis Sullivan, Nicolas Teleman

Topology, vol. 33, no. 4, p. 663–681, 1994, ISSN: 0040-9383.

Résumé

113.

Classifying space for proper actions and ?-theory of group ?*-algebras

Paul Baum, Alain Connes, Nigel Higson

?*-algebras: 1943--1993 (San Antonio, TX, 1993), vol. 167, p. 240–291, Amer. Math. Soc., Providence, RI, 1994.

112.

Interprétation géométrique du modèle standard de la physique des particules et structure fine de l'espace-temps

Alain Connes

C. R. Acad. Sci. Paris Sér. Gén. Vie Sci., vol. 10, no. 3, p. 223–234, 1993, ISSN: 0762-0969.

111.

Formules locales pour les classes de Pontrjagin topologiques

Alain Connes, Dennis Sullivan, Nicolas Teleman

C. R. Acad. Sci. Paris Sér. I Math., vol. 317, no. 5, p. 521–526, 1993, ISSN: 0764-4442.

110.

Transgression and the Chern character of finite-dimensional ?-cycles

Alain Connes, Henri Moscovici

Comm. Math. Phys., vol. 155, no. 1, p. 103–122, 1993, ISSN: 0010-3616.

109.

Editorial (dedication of this issue to Huzihiro Araki)

Alain Connes, Moshé Flato, Heisuke Hironaka, Arthur Jaffe, Vaughan Jones

Comm. Math. Phys., vol. 155, no. 1, p. 1–2, 1993, ISSN: 0010-3616.

108.

Group cohomology with Lipschitz control and higher signatures

Alain Connes, Mikhaïl Gromov, Henri Moscovici

Geom. Funct. Anal., vol. 3, no. 1, p. 1–78, 1993, ISSN: 1016-443X.

107.

Géométrie non commutative et physique quantique

Alain Connes

Mathématiques quantiques, vol. 1992, p. 20, Soc. Math. France, Paris, 1992.

106.

Mathématiques quantiques. Géométrie non commutative et physique quantique. Sur l'équation de Schrödinger.

Alain Connes, Bernard Helffer

Journée annuelle SMF, 23 mai 1992, vol. 1992, p. 52, 1992.

105.

Noncommutative geometry

Alain Connes

In the forest of symbols (Finnish), p. 244–263, Art House, Helsinki, 1992.

104.

Round-table discussion

Alain Connes, Gerd Faltings, Vaughan Jones, Stephen Smale, René Thom, Jorge Wagensberg

Mathematical research today and tomorrow (Barcelona, 1991), vol. 1525, p. 87–108, Springer, Berlin, 1992.

103.

Noncommutative geometry

Alain Connes

Mathematical research today and tomorrow (Barcelona, 1991), vol. 1525, p. 40–58, Springer, Berlin, 1992.

102.

The metric aspect of noncommutative geometry

Alain Connes, John Lott

New symmetry principles in quantum field theory (Carg`ese, 1991), vol. 295, p. 53–93, Plenum, New York, 1992.

101.

Produits eulériens et facteurs de type III

Jean-Benoît Bost, Alain Connes

C. R. Acad. Sci. Paris Sér. I Math., vol. 315, no. 3, p. 279–284, 1992, ISSN: 0764-4442.

100.

Closed star products and cyclic cohomology

Alain Connes, Moshé Flato, Daniel Sternheimer

Lett. Math. Phys., vol. 24, no. 1, p. 1–12, 1992, ISSN: 0377-9017.

99.

Sur la nature de la réalité mathématique

Alain Connes

Elem. Math., vol. 47, no. 1, p. 19–26, 1992, ISSN: 0013-6018.

98.

On the Chern character of ? summable Fredholm modules

Alain Connes

Comm. Math. Phys., vol. 139, no. 1, p. 171–181, 1991, ISSN: 0010-3616.

97.

Caractères des représentations ?-sommables des groupes discrets

Alain Connes

C. R. Acad. Sci. Paris Sér. I Math., vol. 312, no. 9, p. 661–666, 1991, ISSN: 0764-4442.

96.

Particle models and noncommutative geometry

Alain Connes, John Lott

Recent advances in field theory (Annecy-le-Vieux, 1990), vol. 18B, p. 29–47 (1991), 1990, ISSN: 0920-5632.

95.

Essay on physics and noncommutative geometry

Alain Connes

The interface of mathematics and particle physics (Oxford, 1988), vol. 24, p. 9–48, Oxford Univ. Press, New York, 1990.

94.

Géométrie non commutative

Alain Connes

InterEditions, Paris, 1990, ISBN: 2-7296-0284-4.

Résumé

93.

Introduction à la géométrie non-commutative

Alain Connes

The legacy of John von Neumann (Hempstead, NY, 1988), vol. 50, p. 91–118, Amer. Math. Soc., Providence, RI, 1990.

92.

Cyclic cohomology, the Novikov conjecture and hyperbolic groups

Alain Connes, Henri Moscovici

Topology, vol. 29, no. 3, p. 345–388, 1990, ISSN: 0040-9383.

Résumé

91.

Déformations, morphismes asymptotiques et ?-théorie bivariante

Alain Connes, Nigel Higson

C. R. Acad. Sci. Paris Sér. I Math., vol. 311, no. 2, p. 101–106, 1990, ISSN: 0764-4442.

90.

Conjecture de Novikov et fibrés presque plats

Alain Connes, Mikhaïl Gromov, Henri Moscovici

C. R. Acad. Sci. Paris Sér. I Math., vol. 310, no. 5, p. 273–277, 1990, ISSN: 0764-4442.

89.

Matière à pensée

Jean-Pierre Changeux, Alain Connes

Odile Jacob, Paris, 1989, ISBN: 9782738100733.

Résumé

88.

Compact metric spaces, Fredholm modules, and hyperfiniteness

Alain Connes

Ergodic Theory Dynam. Systems, vol. 9, no. 2, p. 207–220, 1989, ISSN: 0143-3857.

87.

Embedding of U(1)-current algebras in noncommutative algebras of classical statistical mechanics

Alain Connes, David E. Evans

Comm. Math. Phys., vol. 121, no. 3, p. 507–525, 1989, ISSN: 0010-3616.

86.

Hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks

Alain Connes, Edward James Woods

Pacific J. Math., vol. 137, no. 2, p. 225–243, 1989, ISSN: 0030-8730.

85.

Noncommutative geometry

Alain Connes

Nonperturbative quantum field theory (Carg`ese, 1987), vol. 185, p. 33–69, Plenum, New York, 1988.

84.

Trace de Dixmier, modules de Fredholm et géométrie riemannienne

Alain Connes

vol. 5B, p. 65–70, 1988, ISSN: 0920-5632, (Conformal field theories and related topics (Annecy-le-Vieux, 1988)).

83.

?-theory for discrete groups

Paul Baum, Alain Connes

Operator algebras and applications, Vol. 1, vol. 135, p. 1–20, Cambridge Univ. Press, Cambridge, 1988.

82.

Caractere multiplicatif d'un module de Fredholm

Alain Connes, Max Karoubi

?-Theory, vol. 2, no. 3, p. 431–463, 1988, ISSN: 0920-3036.

Résumé

81.

Conjecture de Novikov et groupes hyperboliques

Alain Connes, Henri Moscovici

C. R. Acad. Sci. Paris Sér. I Math., vol. 307, no. 9, p. 475–480, 1988, ISSN: 0249-6291.

80.

Cyclic cohomology and noncommutative differential geometry

Alain Connes

Géométrie différentielle (Paris, 1986), vol. 33, p. 33–50, Hermann, Paris, 1988.

79.

Entire cyclic cohomology of Banach algebras and characters of ?-summable Fredholm modules

Alain Connes

?-Theory, vol. 1, no. 6, p. 519–548, 1988, ISSN: 0920-3036.

78.

The action functional in noncommutative geometry

Alain Connes

Comm. Math. Phys., vol. 117, no. 4, p. 673–683, 1988, ISSN: 0010-3616.

77.

Quasi homomorphismes, cohomologie cyclique et positivité

Alain Connes, Joachim Cuntz

Comm. Math. Phys., vol. 114, no. 3, p. 515–526, 1988, ISSN: 0010-3616.

76.

Chern character for discrete groups

Paul Baum, Alain Connes

A fête of topology, p. 163–232, Academic Press, Boston, MA, 1988.

75.

Cyclic cohomology and noncommutative differential geometry

Alain Connes

Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), p. 879–889, Amer. Math. Soc., Providence, RI, 1987.

74.

Dynamical Entropy of ?* Algebras and von Neumann Algebras

Alain Connes, Heide Narnhofer, Walter Thirring

Comm. Math. Phys., vol. 112, no. 4, p. 691–719, 1987, ISSN: 0010-3616.

Résumé

73.

Yang-Mills for noncommutative two-tori

Alain Connes, Marc A. Rieffel

Operator algebras and mathematical physics (Iowa City, Iowa, 1985), vol. 62, p. 237–266, Amer. Math. Soc., Providence, RI, 1987.

72.

Transgression du caractère de Chern et cohomologie cyclique

Alain Connes, Henri Moscovici

C. R. Acad. Sci. Paris Sér. I Math., vol. 303, no. 18, p. 913–918, 1986, ISSN: 0249-6291.

71.

Cyclic cohomology and the transverse fundamental class of a foliation

Alain Connes

Geometric methods in operator algebras (Kyoto, 1983), vol. 123, p. 52–144, Longman Sci. Tech., Harlow, 1986.

Résumé

70.

Indice des sous facteurs, algèbres de Hecke et théorie des nœuds (d'après Vaughan Jones)

Alain Connes

no. 133-134, p. 289–308, 1986, ISSN: 0303-1179, (Seminar Bourbaki, Vol. 1984/85).

69.

Leafwise homotopy equivalence and rational Pontrjagin classes

Paul Baum, Alain Connes

Foliations (Tokyo, 1983), vol. 5, p. 1–14, North-Holland, Amsterdam, 1985.

68.

Noncommutative differential geometry

Alain Connes

Inst. Hautes Études Sci. Publ. Math., no. 62, p. 257–360, 1985, ISSN: 0073-8301.

Résumé

67.

Diameters of state spaces of type III factors

Alain Connes, Uffe Haagerup, Erling Størmer

Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), vol. 1132, p. 91–116, Springer, Berlin, 1985.

66.

Entropie de Kolmogoroff-Sinai et mécanique statistique quantique

Alain Connes

C. R. Acad. Sci. Paris Sér. I Math., vol. 301, no. 1, p. 1–6, 1985, ISSN: 0249-6291.

65.

Introduction to noncommutative differential geometry

Alain Connes

Workshop Bonn 1984 (Bonn, 1984), vol. 1111, p. 3–16, Springer, Berlin, 1985.

64.

Approximately transitive flows and ITPFI factors

Alain Connes, Edward James Woods

Ergodic Theory Dynam. Systems, vol. 5, no. 2, p. 203–236, 1985, ISSN: 0143-3857.

63.

Factors of type III₁, property ?'λ and closure of inner automorphisms

Alain Connes

J. Operator Theory, vol. 14, no. 1, p. 189–211, 1985, ISSN: 0379-4024.

62.

Property T for von Neumann algebras

Alain Connes, Vaughan Jones

Bull. London Math. Soc., vol. 17, no. 1, p. 57–62, 1985, ISSN: 0024-6093.

61.

The longitudinal index theorem for foliations

Alain Connes, Georges Skandalis

Publ. Res. Inst. Math. Sci., vol. 20, no. 6, p. 1139–1183, 1984, ISSN: 0034-5318.

Résumé

60.

Caractère multiplicatif d'un module de Fredholm

Alain Connes, Max Karoubi

C. R. Acad. Sci. Paris Sér. I Math., vol. 299, no. 19, p. 963–968, 1984, ISSN: 0249-6291.

59.

A connection between the classical and the quantum mechanical entropies

Alain Connes, Erling Størmer

Operator algebras and group representations, Vol. I (Neptun, 1980), vol. 17, p. 113–123, Pitman, Boston, MA, 1984.

58.

Cohomologie cyclique et foncteurs Ext?

Alain Connes

C. R. Acad. Sci. Paris Sér. I Math., vol. 296, no. 23, p. 953–958, 1983, ISSN: 0249-6291.

Résumé

57.

A survey of foliations and operator algebras

Alain Connes

Operator algebras and applications, Part I (Kingston, Ont., 1980), vol. 38, p. 521–628, Amer. Math. Soc., Providence, R.I., 1982.

Résumé

56.

?²-index theory on homogeneous spaces and discrete series representations

Alain Connes, Henri Moscovici

Operator algebras and applications, Part I (Kingston, Ont., 1980), vol. 38, p. 419–433, Amer. Math. Soc., Providence, R.I., 1982.

55.

Classification des facteurs

Alain Connes

Operator algebras and applications, Part 2 (Kingston, Ont., 1980), vol. 38, p. 43–109, Amer. Math. Soc., Providence, R.I., 1982.

54.

The ?²-index theorem for homogeneous spaces of Lie groups

Alain Connes, Henri Moscovici

Ann. of Math. (2), vol. 115, no. 2, p. 291–330, 1982, ISSN: 0003-486X.

53.

A II₁ factor with two nonconjugate Cartan subalgebras

Alain Connes, Vaughan Jones

Bull. Amer. Math. Soc. (N.S.), vol. 6, no. 2, p. 211–212, 1982, ISSN: 0273-0979.

52.

An amenable equivalence relation is generated by a single transformation

Alain Connes, Jacob Feldman, Benjamin Weiss

Ergodic Theory Dynam. Systems, vol. 1, no. 4, p. 431–450 (1982), 1981, ISSN: 0143-3857.

51.

Feuilletages et algèbres d'opérateurs

Alain Connes

Bourbaki Seminar, Vol. 1979/80, vol. 842, p. 139–155, Springer, Berlin-New York, 1981.

50.

Théorème de l'indice pour les feuilletages

Alain Connes, Georges Skandalis

C. R. Acad. Sci. Paris Sér. I Math., vol. 292, no. 18, p. 871–876, 1981, ISSN: 0249-6291.

49.

An analogue of the Thom isomorphism for crossed products of a ?*-algebra by an action of ℝ

Alain Connes

Adv. in Math., vol. 39, no. 1, p. 31–55, 1981, ISSN: 0001-8708.

48.

Property T and asymptotically invariant sequences

Alain Connes, Benjamin Weiss

Israel J. Math., vol. 37, no. 3, p. 209–210, 1980, ISSN: 0021-2172.

47.

A factor of type II₁ with countable fundamental group

Alain Connes

J. Operator Theory, vol. 4, no. 1, p. 151–153, 1980, ISSN: 0379-4024.

46.

A construction of approximately finite-dimensional non-ITPFI factors

Alain Connes, Edward James Woods

Canad. Math. Bull., vol. 23, no. 2, p. 227–230, 1980, ISSN: 0008-4395.

45.

?*-algèbres et géométrie différentielle

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 290, no. 13, p. A599–A604, 1980, ISSN: 0151-0509.

Résumé

44.

Von Neumann algebras

Alain Connes

Proceedings of the International Congress of Mathematicians (Helsinki, 1978), p. 97–109, Acad. Sci. Fennica, Helsinki, 1980.

43.

On the spatial theory of von Neumann algebras

Alain Connes

J. Functional Analysis, vol. 35, no. 2, p. 153–164, 1980, ISSN: 0022-1236.

42.

On the equivalence between injectivity and semidiscreteness for operator algebras

Alain Connes

Algèbres d'opérateurs et leurs applications en physique mathématique (Proc. Colloq., Marseille, 1977), p. 107–112, CNRS, Paris, 1979.

41.

Sur la théorie non commutative de l'intégration

Alain Connes

Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978), vol. 725, p. 19–143, Springer, Berlin, 1979.

Résumé

40.

The ?²-index theorem for homogeneous spaces

Alain Connes, Henri Moscovici

Bull. Amer. Math. Soc. (N.S.), vol. 1, no. 4, p. 688–690, 1979, ISSN: 0273-0979.

39.

The von Neumann algebra of a foliation

Alain Connes

Mathematical problems in theoretical physics (Proc. Internat. Conf., Univ. Rome, Rome, 1977), p. 145–151, Springer, Berlin-New York, 1978.

38.

Errata: "The flow of weights on factors of type III"

Alain Connes, Masamichi Takesaki

Tohoku Math. J. (2), vol. 30, no. 4, p. 653–655, 1978, ISSN: 0040-8735.

37.

On the cohomology of operator algebras

Alain Connes

J. Functional Analysis, vol. 28, no. 2, p. 248–253, 1978.

36.

Homogeneity of the state space of factors of type III₁

Alain Connes, Erling Størmer

J. Functional Analysis, vol. 28, no. 2, p. 187–196, 1978.

35.

The flow of weights on factors of type III

Alain Connes, Masamichi Takesaki

Tohoku Math. J. (2), vol. 29, no. 4, p. 473–575, 1977, ISSN: 0040-8735.

34.

Periodic automorphisms of the hyperfinite factor of type II₁

Alain Connes

Acta Sci. Math. (Szeged), vol. 39, no. 1-2, p. 39–66, 1977, ISSN: 0001-6969.

Résumé

33.

Measure space automorphisms, the normalizers of their full groups, and approximate finiteness

Alain Connes, Wolfgang Krieger

J. Functional Analysis, vol. 24, no. 4, p. 336–352, 1977.

32.

The Tomita-Takesaki theory and classification of type-III factors

Alain Connes

?*-algebras and their applications to statistical mechanics and quantum field theory (Proc. Internat. School of Physics "Enrico Fermi", Course LX, Varenna, 1973), p. 29–46, 1976.

31.

Classification of injective factors. Cases II₁, II, IIIλ, λ ≠ 1

Alain Connes

Ann. of Math. (2), vol. 104, no. 1, p. 73–115, 1976, ISSN: 0003-486X.

30.

On the classification of von Neumann algebras and their automorphisms

Alain Connes

Symposia Mathematica, Vol. XX (Convegno sulle Algebre ?* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria ?, INDAM, Rome, 1975), p. 435–478, 1976.

29.

Outer conjugacy of automorphisms of factors

Alain Connes

Symposia Mathematica, Vol. XX (Convegno sulle Algebre ?* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria ?, INDAM, Rome, 1975), p. 149–159, 1976.

28.

Entropy for automorphisms of II₁ von Neumann algebras

Alain Connes, Erling Størmer

Acta Math., vol. 134, no. 3-4, p. 289–306, 1975, ISSN: 0001-5962.

27.

Structure theory for Type III factors

Alain Connes

Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, p. 87–91, 1975.

26.

A factor not anti-isomorphic to itself

Alain Connes

Bull. London Math. Soc., vol. 7, p. 171–174, 1975, ISSN: 0024-6093.

25.

On the hierarchy of W. Krieger

Alain Connes

Illinois J. Math., vol. 19, p. 428–432, 1975, ISSN: 0019-2082.

24.

Outer conjugacy classes of automorphisms of factors

Alain Connes

Ann. Sci. École Norm. Sup. (4), vol. 8, no. 3, p. 383–419, 1975, ISSN: 0012-9593.

Résumé

23.

Classification of automorphisms of hyperfinite factors of type II₁ and II and application to type III factors

Alain Connes

Bull. Amer. Math. Soc., vol. 81, no. 6, p. 1090–1092, 1975, ISSN: 0002-9904.

22.

Sur la classification des facteurs de type II

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 281, no. 1, p. Aii, A13–A15, 1975, ISSN: 0151-0509.

21.

On hyperfinite factors of type III₀ and Krieger's factors

Alain Connes

J. Functional Analysis, vol. 18, p. 318–327, 1975.

20.

A factor not anti-isomorphic to itself

Alain Connes

Ann. of Math. (2), vol. 101, p. 536–554, 1975, ISSN: 0003-486X.

19.

Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann

Alain Connes

Ann. Inst. Fourier (Grenoble), vol. 24, no. 4, p. x, 121–155 (1975), 1974, ISSN: 0373-0956.

Résumé

18.

Existence de facteurs infinis asymtotiquement abéliens

Alain Connes, Edward James Woods

C. R. Acad. Sci. Paris Sér. A, vol. 279, p. 189–191, 1974, ISSN: 0302-8429.

17.

Almost periodic states and factors of type III₁

Alain Connes

J. Functional Analysis, vol. 16, p. 415–445, 1974.

16.

Flots des poids sur les facteurs de type III

Alain Connes, Masamichi Takesaki

C. R. Acad. Sci. Paris Sér. A, vol. 278, p. 945–948, 1974, ISSN: 0302-8429.

15.

Sur le théorème de Radon-Nikodym pour les poids normaux fidèles semi-finis

Alain Connes

Bull. Sci. Math. (2), vol. 97, p. 253–258 (1974), 1973, ISSN: 0007-4497.

14.

Une classification des facteurs de type III

Alain Connes

Ann. Sci. École Norm. Sup. (4), vol. 6, p. 133–252, 1973, ISSN: 0012-9593.

13.

The group property of the invariant ? of von Neumann algebras

Alain Connes, Alfons van Daele

Math. Scand., vol. 32, p. 187–192 (1974), 1973, ISSN: 0025-5521.

12.

Ordres faibles et localisation de zéros de polynômes

Alain Connes

Séminaire Delange-Pisot-Poitou (12e année: 1970/71), Théorie des nombres, Exp. No. 18, p. 11, 1972.

11.

Une classification des facteurs de type III

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 275, p. A523–A525, 1972, ISSN: 0151-0509.

10.

Groupe modulaire d'une algèbre de von Neumann

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 274, p. A1923–A1926, 1972, ISSN: 0151-0509.

9.

États presque périodiques sur une algèbre de von Neumann

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 274, p. A1402–A1405, 1972, ISSN: 0151-0509.

8.

Calcul des deux invariants d'Araki et Woods par la théorie de Tomita et Takesaki

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 274, p. A175–A177, 1972, ISSN: 0151-0509.

7.

Un théorème de décomposition d'applications mesurables

Alain Connes

Séminaire Choquet, 10e année (1970/71), Initiation à l'analyse, Fasc. 1, Exp. No. 12, p. 7, 1971.

6.

Un nouvel invariant pour les algèbres de von Neumann

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 273, p. A900–A903, 1971, ISSN: 0151-0509.

5.

Ultrapuissances et applications dans le cadre de l'analyse non standard

Alain Connes

Séminaire Choquet: 1969/70, Initiation `a lÁnalyse, p. Fasc. 1, Exp. 8, 25, Secrétariat mathématique, Paris, 1970.

4.

Détermination de modèles minimaux en analyse non standard et application

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 271, p. A969–A971, 1970, ISSN: 0151-0509.

3.

Ordres faibles et localisation de zéros de polynômes

Alain Connes

Séminaire Choquet: 1968/69, Initiation à l'Analyse, Exp. 5, p. 27, Secrétariat mathématique, Paris, 1969.

2.

Ordres faibles et localisation des zéros de polynomes

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 269, p. A373–A376, 1969, ISSN: 0151-0509.

1.

Sur une généralisation de la notion de corps ordonné

Alain Connes

C. R. Acad. Sci. Paris Sér. A-B, vol. 269, p. A337–A340, 1969, ISSN: 0151-0509.