Alain Connes의 정보
수상나이 35
출생년도 1947
사망년도
출생지 Darguignan(France)
현재소속 Institut des Hautes ?tudes Scientifiques
연구실적 [자세히 보기]
관련출판물 1.H Araki, The work of Alain Connes, Proceedings of the International Congress of Mathematicians, Warsaw, 1983 1 (Warsaw, 1984), 3-10.

2.H Araki, Profiles of 1982 Fields Medal winners (Japanese), Sugaku 35 (1) (1983), 70-77.

3.J Mi, The work of mathematicians awarded the Fields Medal in 1983 and 1986 (Chinese), J. Northwest Univ. 19 (1) (1989), 103-104.

4.C C Moore, The work of Alain Connes, Notices Amer. Math. Soc. 29 (1982), 499-501.

5.A K Seda, One aspect of the work of Alain Connes, Irish Math. Soc. Newslett. No. 11 (1984), 38-48.

시상내역 Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general.
Other Award Prix Aimee Berthe(1975), Prix Pecot-Vimont(1976), Gold medal of the Centre National de la Recherche Scientifique(1977), Prix Ampere(1980), Prix de Electricite(1981)
연구단행본 [1] Connes, A.; Kreimer, D. From local perturbation theory to Hopf- and Lie-algebras of Feynman graphs. Mathematical physics in mathematics and physics (Siena, 2000), 105--114, Fields Inst. Commun., 30, Amer. Math. Soc., Providence, RI, 2001. 81T18 (16W30 81Q30 81T15)
[2] Connes, Alain; Lichnerowicz, André; Schützenberger, Marcel Paul Triangle of thoughts. Translated from the 2000 French original by Jennifer Gage. American Mathematical Society, Providence, RI, 2001. viii+179 pp. ISBN: 0-8218-2614-X 00A05 (00A79 01A05)
[3] Connes, Alain Noncommutative geometry and the Riemann zeta function. Mathematics: frontiers and perspectives, 35--54, Amer. Math. Soc., Providence, RI, 2000. 11S31 (11-02 11M36 46L87 58B34)
[4] Connes, A.; Kreimer, D. Hopf algebras, renormalization and noncommutative geometry. Quantum field theory: perspective and prospective (Les Houches, 1998), 59--108, NATO Sci. Ser. C Math. Phys. Sci., 530, Kluwer Acad. Publ., Dordrecht, 1999. 81R60 (16W30 81T15 81T75)
[5] GAFA 2000. Visions in mathematics. Towards 2000. Proceedings of the meeting held at Tel Aviv University, Tel Aviv, August 25--September 3, 1999. Edited by N. Alon, J. Bourgain, A. Connes, M. Gromov and V. Milman. Geom. Funct. Anal. 2000, Special Volume, Part II. Birkhäuser Verlag, Basel, 2000. pp. i--viii and 455--983. 00B25
[6] GAFA 2000. Visions in mathematics. Towards 2000. Proceedings of the meeting held at Tel Aviv University, Tel Aviv, August 25--September 3, 1999. Edited by N. Alon, J. Bourgain, A. Connes, M. Gromov and V. Milman. Geom. Funct. Anal. 2000, Special Volume, Part I. Birkhäuser Verlag, Basel, 2000. pp. i--xiv and 1--453. 00B25
[7] Connes, Alain Hypoelliptic operators, Hopf algebras and cyclic cohomology. Algebraic $K$-theory and its applications (Trieste, 1997), 164--205, World Sci. Publishing, River Edge, NJ, 1999. 58J42 (16E40 19D55)
[8] Connes, Alain Trace formula on the adèle class space and Weil positivity. Current developments in mathematics, 1997 (Cambridge, MA), 5--64, Int. Press, Boston, MA, 1999. 11R56 (11M26 11R37 11S45 46L35)
[9] Connes, Alain Noncommutative geometry: the spectral aspect. Symétries quantiques (Les Houches, 1995), 643--686, North-Holland, Amsterdam, 1998. 58J42 (46L87 58B34 58J22)
[10] Connes, Alain A new proof of Morley's theorem. Les relations entre les mathématiques et la physique théorique, 43--46, Inst. Hautes Études Sci., Bures-sur-Yvette, 1998. 51M04
[11] Symétries quantiques. [Quantum symmetries] Papers from the NATO Advanced Study Institute held at the 64th Session of the Summer School in Theoretical Physics in Les Houches, August 1--September 8, 1995. Edited by A. Connes, K. Gawedzki and J. Zinn-Justin. North-Holland Publishing Co., Amsterdam, 1998. xxxviii+990 pp. ISBN: 0-444-82867-2 81-06 (58-06)
[12] Connes, Alain Noncommutative differential geometry and the structure of space time. Operator algebras and quantum field theory (Rome, 1996), 330--358, Internat. Press, Cambridge, MA, 1997. 58B30 (19K56 46L87 58G10 58G12)
[13] Connes, Alain Noncommutative differential geometry and the structure of space-time. The geometric universe (Oxford, 1996), 49--80, Oxford Univ. Press, Oxford, 1998. 58B30 (19K56 46L87 58G10 58G12)
[14] Connes, Alain Noncommutative differential geometry and the structure of space time. Quantum fields and quantum space time (Cargèse, 1996), 45--72, NATO Adv. Sci. Inst. Ser. B Phys., 364, Plenum, New York, 1997. 58B30 (19K56 46L87 58G10 58G12)
[15] Connes, Alain Noncommutative differential geometry and the structure of space time. Deformation theory and symplectic geometry (Ascona, 1996), 1--33, Math. Phys. Stud., 20, Kluwer Acad. Publ., Dordrecht, 1997. 58B30 (19K56 46L87 58G10 58G12 81R40)
[16] Connes, Alain; Douglas, Michael R.; Schwarz, Albert Noncommutative geometry and matrix theory: compactification on tori. J. High Energy Phys. 1998, no. 2, Paper 3, 35 pp. (electronic). 58B30 (81T30)
[17] Connes, A. Géométrie non commutative et physique quantique. (French) [Noncommutative geometry and quantum physics] Mathématiques quantiques, 20 pp., SMF Journ. Annu., 1992, Soc. Math. France, Paris, 1992. 58B30 (46L60 46L87 81V22 81V70)
[18] Connes, Alain Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Journées "Équations aux Dérivées Partielles" (Saint-Jean-de-Monts, 1997), Exp. No. IV, 28 pp., École Polytech., Palaiseau, 1997. 11M26 (46L87 58B30)
[19] Connes, Alain Brisure de symétrie spontanée et géométrie du point de vue spectral. (French) [Spontaneous symmetry breaking and geometry from the spectral point of view] Séminaire Bourbaki, Vol. 1995/96. Astérisque No. 241 (1997), Exp. No. 816, 5, 313--349. 58B30 (19K56 46L87 58G10 58G12 81R40)
[20] Connes, A. Non-commutative geometry and physics. Gravitation et quantifications (Les Houches, 1992), 805--950, North-Holland, Amsterdam, 1995. 58B30 (46L87 81T13 81V22)
[21] Connes, Alain; Helffer, Bernard Mathématiques quantiques. (French) [Quantum mathematics] SMF Journée Annuelle [SMF Annual Conference], 1992. Société Mathématique de France, Paris, 1992. 52 pp. 81-06
[22] Connes, Alain Quantized calculus and applications. XIth International Congress of Mathematical Physics (Paris, 1994), 15--36, Internat. Press, Cambridge, MA, 1995. 58B30 (46L87 58G15 81T30)
[23] Baum, Paul; Connes, Alain; Higson, Nigel Classifying space for proper actions and $K$-theory of group $C\sp *$-algebras. $C\sp *$-algebras: 1943--1993 (San Antonio, TX, 1993), 240--291, Contemp. Math., 167, Amer. Math. Soc., Providence, RI, 1994. 46L80 (19K56 22D25 46L85)
[24] Changeux, Jean-Pierre; Connes, Alain Conversations on mind, matter, and mathematics. Edited and translated from the 1989 French original by M. B. DeBevoise. Princeton University Press, Princeton, NJ, 1995. xii+261 pp. ISBN: 0-691-08759-8 00A30 (00A69)
[25] Connes, Alain Noncommutative geometry. Academic Press, Inc., San Diego, CA, 1994. xiv+661 pp. ISBN: 0-12-185860-X 46Lxx (19K56 22D25 58B30 58G12 81T13 81V22 81V70)
[26] Changeux, Jean-Pierre; Connes, Alain Matière à pensée. (French) [Food for thought] Reprint of the 1989 edition. Points. Editions Odile Jacob, Paris, 1992. 268 pp. ISBN: 2-02-014676-2 00A30 (00A69)
[27] Enock, Michel; Schwartz, Jean-Marie Kac algebras and duality of locally compact groups. With a preface by Alain Connes. With a postface by Adrian Ocneanu. Springer-Verlag, Berlin, 1992. x+257 pp. ISBN: 3-540-54745-2 46-02 (22D25 22D35 43A65 46L10 46M99)
[28] Changeux, Jean-Pierre; Connes, Alain Materia de reflexión. (Spanish) [Food for thought] Translated from the French by Marc Noy. Metatemas, 30. Tusquets Editores, S.A., Barcelona, 1993. 196 pp. ISBN: 84-7223-661-7 00A30 (00A69 92B05 92B20)
[29] Connes, Alain; Lott, John The metric aspect of noncommutative geometry. New symmetry principles in quantum field theory (Cargèse, 1991), 53--93, NATO Adv. Sci. Inst. Ser. B Phys., 295, Plenum, New York, 1992. 58B30 (22E40 46L87 81T60 81V22)
[30] Connes, A. Essay on physics and noncommutative geometry. The interface of mathematics and particle physics (Oxford, 1988), 9--48, Inst. Math. Appl. Conf. Ser. New Ser., 24, Oxford Univ. Press, New York, 1990. 58B30 (19D55 46L87 81T10)
[31] Connes, Alain Introduction à la géométrie non-commutative. (French) [Introduction to noncommutative geometry] The legacy of John von Neumann (Hempstead, NY, 1988), 91--118, Proc. Sympos. Pure Math., 50, Amer. Math. Soc., Providence, RI, 1990. 58B30 (19K56 46L87 57R30)
[32] Connes, Alain Géométrie non commutative. (French) [Noncommutative geometry] InterEditions, Paris, 1990. 240 pp. ISBN: 2-7296-0284-4 58B30 (19K56 46L85 46L87 46L89 58G12 81T99)
[33] Connes, Alain Noncommutative geometry. Nonperturbative quantum field theory (Cargèse, 1987), 33--69, NATO Adv. Sci. Inst. Ser. B Phys., 185, Plenum, New York, 1988. 58G12 (19D55 19K56 46Lxx 58B30)
[34] Operator algebras, unitary representations, enveloping algebras, and invariant theory. Papers from the colloquium in honor of Jacques Dixmier held at the Institut Henri Poincaré, Paris, May 22--26, 1989. Edited by Alain Connes, Michel Duflo, Anthony Joseph and Rudolf Rentschler. Progress in Mathematics, 92. Birkhäuser Boston, Inc., Boston, MA, 1990. xviii+579 pp. ISBN: 0-8176-3489-4 00B25 (22-06 46-06 46Lxx)
[35] Baum, Paul; Connes, Alain $K$-theory for discrete groups. Operator algebras and applications, Vol. 1, 1--20, London Math. Soc. Lecture Note Ser., 135, Cambridge Univ. Press, Cambridge, 1988. 46L80 (19K99 22E40 58G12)
[36] Baum, Paul; Connes, Alain Chern character for discrete groups. A fête of topology, 163--232, Academic Press, Boston, MA, 1988. 58G12 (19L10 19L47 55N91)
[37] Connes, A. Trace de Dixmier, modules de Fredholm et géométrie riemannienne. (French) [Dixmier trace, Fredholm modules and Riemannian geometry] Conformal field theories and related topics (Annecy-le-Vieux, 1988). Nuclear Phys. B Proc. Suppl. 5B (1988), 65--70. 58B15 (17B65 46L99 58G12)
[38] Connes, Alain Cyclic cohomology and noncommutative differential geometry. Géométrie différentielle (Paris, 1986), 33--50, Travaux en Cours, 33, Hermann, Paris, 1988. 58G12 (18G10 18G25 19K56 46L80 46M20)
[39] Connes, A. Cyclic cohomology and noncommutative differential geometry. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 879--889, Amer. Math. Soc., Providence, RI, 1987. 58G12 (19D55 19K56 46L80 57R20 57R30)
[40] Kastler, Daniel Cyclic cohomology within the differential envelope. An introduction to Alain Connes' noncommutative differential geometry. Travaux en Cours [Works in Progress], 30. Hermann, Paris, 1988. viii+184 pp. ISBN: 2-7056-6044-5 18F25 (16A62 17B35 19D55 58A12)
[41] Connes, A. Cyclic cohomology and the transverse fundamental class of a foliation. Geometric methods in operator algebras (Kyoto, 1983), 52--144, Pitman Res. Notes Math. Ser., 123, Longman Sci. Tech., Harlow, 1986. 58G12 (19K56 19L64 46L80 53C12 57R30 57R32)
[42] Baum, Paul; Connes, Alain Leafwise homotopy equivalence and rational Pontrjagin classes. Foliations (Tokyo, 1983), 1--14, Adv. Stud. Pure Math., 5, North-Holland, Amsterdam, 1985. 58G12 (57R30 58H10)
[43] Connes, Alain; Rieffel, Marc A. Yang-Mills for noncommutative two-tori. Operator algebras and mathematical physics (Iowa City, Iowa, 1985), 237--266, Contemp. Math., 62, Amer. Math. Soc., Providence, RI, 1987. 58E15 (18F25 19K99 46L99 46M20 58G12 58G40)
[44] Connes, Alain; Haagerup, Uffe; Størmer, Erling Diameters of state spaces of type ${\rm III}$ factors. Operator algebras and their connections with topology and ergodic theory (Bu\c steni, 1983), 91--116, Lecture Notes in Math., 1132, Springer, Berlin, 1985. 46L35
[45] Connes, A. Introduction to noncommutative differential geometry. Workshop Bonn 1984 (Bonn, 1984), 3--16, Lecture Notes in Math., 1111, Springer, Berlin, 1985. 58G12 (18F25 19D55 46L50 57R30 58G10)
[46] Connes, A.; Størmer, E. A connection between the classical and the quantum mechanical entropies. Operator algebras and group representations, Vol. I (Neptun, 1980), 113--123, Monogr. Stud. Math., 17, Pitman, Boston, MA, 1984. 46L40 (46L60 82A15)
[47] Connes, A. A survey of foliations and operator algebras. Operator algebras and applications, Part I (Kingston, Ont., 1980), pp. 521--628, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982. 58G12 (22E25 46L50 57R30 58F18 58G10)
[48] Connes, A. Classification des facteurs. (French) [Classification of factors] Operator algebras and applications, Part 2 (Kingston, Ont., 1980), pp. 43--109, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982. 46L35 (22D25 46L55)
[49] Connes, Alain; Moscovici, Henri $L\sp{2}$-index theory on homogeneous spaces and discrete series representations. Operator algebras and applications, Part I (Kingston, Ont., 1980), pp. 419--433, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982. 58G10 (22E45 46M20)
[50] Connes, Alain Feuilletages et algèbres d'opérateurs. (French) [Foliations and operator algebras] Bourbaki Seminar, Vol. 1979/80, pp. 139--155, Lecture Notes in Math., 842, Springer, Berlin-New York, 1981. 58G12 (46L99 46M20 57R30)
[51] Connes, A. von Neumann algebras. Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 97--109, Acad. Sci. Fennica, Helsinki, 1980. 46L10 (46-03)
[52] Connes, Alain Sur la théorie non commutative de l'intégration. (French) Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978), pp. 19--143, Lecture Notes in Math., 725, Springer, Berlin, 1979. 46L50 (22E46 58G10 58G12)
[53] Connes, A. On the equivalence between injectivity and semidiscreteness for operator algebras. Algèbres d'opérateurs et leurs applications en physique mathématique (Proc. Colloq., Marseille, 1977), pp. 107--112, Colloq. Internat. CNRS, 274, CNRS, Paris, 1979. 46L10
[54] Connes, Alain The von Neumann algebra of a foliation. Mathematical problems in theoretical physics (Proc. Internat. Conf., Univ. Rome, Rome, 1977), pp. 145--151, Lecture Notes in Phys., 80, Springer, Berlin-New York, 1978. 46L55 (46L10 58G12)
[55] Connes, A. The Tomita-Takesaki theory and classification of type-III factors. $C\sp*$-algebras and their applications to statistical mechanics and quantum field theory (Proc. Internat. School of Physics "Enrico Fermi", Course LX, Varenna, 1973), pp. 29--46. North-Holland, Amsterdam, 1976. 46L10
[56] Connes, Alain Un théorème de décomposition d'applications mesurables. (French) Séminaire Choquet, 10e année (1970/71), Initiation à l'analyse, Fasc. 1, Exp. No. 12, 7 pp. Secrétariat Mathématique, Paris, 1971. 46G15 (28A50)
[57] Ajlani, Marouan Les cônes autopolaires en dimension finie. (French) D'après Alain Connes (Ann. Inst. Fourier (Grenoble) 24 (1974), fasc. 4, x, 121--155 (1975)). Séminaire Choquet, 14e année (1974/75), Initiation à l'analyse, Exp. No. 18, 8 pp. Secrétariat Mathématique, Paris, 1975. 32M10
[58] Connes, A. On the classification of von Neumann algebras and their automorphisms. Symposia Mathematica, Vol. XX (Convegno sulle Algebre $C\sp*$ e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria $K$, INDAM, Rome, 1975), pp. 435--478. Academic Press, London, 1976. 46L10
[59] Connes, A. Outer conjugacy of automorphisms of factors. Symposia Mathematica, Vol. XX (Convegno sulle Algebre $C\sp*$ e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria $K$, INDAM, Rome, 1975), pp. 149--159. Academic Press, London, 1976. 46L10
[60] Combes, François Les facteurs de von Neumann de type III (d'après A. Connes). (French) Séminaire Bourbaki (1974/1975: Exposés Nos. 453-470), Exp. No. 461, pp. 124--137. Lecture Notes in Math., Vol. 514, Springer, Berlin, 1976. 46L10
[61] Connes, A. Structure theory for Type III factors. Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, pp. 87--91. Canad. Math. Congress, Montreal, Que., 1975. 46L10
[62] Connes, Alain Ordres faibles et localisation de zéros de polynômes. Séminaire Delange-Pisot-Poitou (12e année: 1970/71), Théorie des nombres, Exp. No. 18, 11 pp. Secrétariat Mathématique, Paris, 1972. 12D10
[63] Pathiaux, Martine Détermination effective des polynômes de A. Connes relativement à un nombre de Pisot. (French) Séminaire Delange-Pisot-Poitou (13e année: 1971/72), Théorie des nombres, Fasc. 2, Exp. No. G5, 3 pp. Secrétariat Mathématique, Paris, 1973. 12D10
[64] Connes, Alain Ultrapuissances et applications dans le cadre de l'analyse non standard. (French) 1970 Séminaire Choquet: 1969/70, Initiation à l'Analyse Fasc. 1, Exp. 8, 25 pp. Secrétariat mathématique, Paris 02.57 (54.00)
[65] Connes, Alain Ordres faibles et localisation de zéros de polynômes. (French) 1969 Séminaire Choquet: 1968/69, Initiation à l'Analyse, Exp. 5 27 pp. Secrétariat mathématique, Paris 12.30
[66] Connes, Alain; Moscovici, Henri Cyclic cohomology and Hopf algebra symmetry [1800488]. Conférence Moshé Flato 1999, Vol. I (Dijon), 121--147, Math. Phys. Stud., 21, Kluwer Acad. Publ., Dordrecht, 2000. 58B34 (19D55 46L85 46L87 58B32 81R60)
[67] Connes, Alain Brisure de symétrie spontanée et géométrie du point de vue spectral [MR 98h:58011a; MR 98h:58011b]. (French) [Spontaneous symmetry breaking and geometry from the spectral point of view] Fields Medallists' lectures, 340--371, World Sci. Ser. 20th Century Math., 5, World Sci. Publishing, River Edge, NJ, 1997. 58B30
[68] Araki, Huzihiro The work of Alain Connes [MR 87c:46064]. Fields Medallists' lectures, 329--336, World Sci. Ser. 20th Century Math., 5, World Sci. Publishing, River Edge, NJ, 1997. 01A70 (46-03)
[69] Connes, Alain Noncommutative differential geometry and the structure of space time. Cyclic cohomology and noncommutative geometry (Waterloo, ON, 1995), 17--42, Fields Inst. Commun., 17, Amer. Math. Soc., Providence, RI, 1997. 83C65 (58B34 58J42 81T75)
[70] Connes, Alain Noncommutative geometry. (Finnish) In the forest of symbols (Finnish), 244--263, Art House, Helsinki, 1992. 46Lxx (19Kxx 22D25 58Bxx 58G12 81Txx 81Vxx)
[71] Lebowitz, J.; Atiyah, M.; Brézin, E.; Connes, A.; Fröhlich, J.; Gross, D.; Jaffe, A.; Kadanoff, L.; Ruelle, D. Round table: physics and mathematics. XIth International Congress of Mathematical Physics (Paris, 1994), 691--705, Internat. Press, Cambridge, MA, 1995. 00A79 (00A30)
[72] Connes, Alain; Faltings, Gerd; Jones, Vaughan; Smale, Stephen; Thom, René; Wagensberg, Jorge Round-table discussion. Mathematical research today and tomorrow (Barcelona, 1991), 87--108, Lecture Notes in Math., 1525, Springer, Berlin, 1992. 00A05
[73] Connes, Alain Noncommutative geometry. Mathematical research today and tomorrow (Barcelona, 1991), 40--58, Lecture Notes in Math., 1525, Springer, Berlin, 1992. 46L89 (46-02 46L85 46L87 58B30)
연구논문
  • Connes, Alain;Kreimer, Dirk   From local perturbation theory to Hopf and Lie algebras of Feynman graphs   Lett. Math. Phys.   56   1   (2001)   3-15   81T15, 17Bxx, 81T17, 81T18
  • Connes, Alain;Landi, Giovanni   Noncommutative manifolds, the instanton algebra and isospectral deformations   Comm. Math. Phys.   221   1   (2001)   141-159   81R60, 57Rxx, 58B34, 58J42, 81T75
  • Connes, Alain   A lecture on noncommutative geometry. Mathematics towards the third millennium   Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.     Special Is   (2000)   31-64   58B34, 46L87, 58J42
  • Connes, Alain   Noncommutative geometry---year 2000   Geom. Funct. Anal.   Special Volume, II     (2000)   481-559   58B34, 00A05, 19K56, 46L87
  • Connes, Alain;Kreimer, Dirk   Renormalization in quantum field theory and the Riemann-Hilbert problem. II. The $beta$-function, diffeomorphisms and the renormalization group   Comm. Math. Phys.   216   1   (2001)   215-241   81Txx, 34Mxx
  • Connes, Alain;Kreimer, Dirk   Renormalization in quantum field theory and the Riemann-Hilbert problem I: The Hopf algebra structure of graphs and the main theorem   Comm. Math. Phys.   210   1   (2000)   249-273   81Txx, 34M50
  • Connes, Alain;Moscovici, Henri   Cyclic cohomology and Hopf algebra symmetry   Lett. Math. Phys.   52   1   (2000)   1-28   58B34, 16W30, 19D55, 46L87, 58B32
  • Connes, Alain   A short survey of noncommutative geometry   J. Math. Phys.   41   6   (2000)   3832-3866   58B34, 46L87, 58J42, 81R60, 81T15, 81T18, 81T75
  • Connes, Alain;Kreimer, Dirk   Renormalization in quantum field theory and the Riemann-Hilbert problem   J. High Energy Phys.     9   (1999)   8   81T15, 16W30, 81T75
  • Baum, Paul;Connes, Alain   Geometric $K$-theory for Lie groups and foliations   Enseign. Math. (2)   46   1-2   (2000)   3-42   19K56, 22D25, 46L80, 46L87, 58J22
  • Connes, Alain;Kreimer, Dirk   Lessons from quantum field theory: Hopf algebras and spacetime geometries. Mosh? Flato (1937--1998)   Lett. Math. Phys.   48   1   (1999)   85-96   81T15, 16W30, 46L87, 58B34, 81-02, 81T18
  • Connes, Alain;Moscovici, Henri   Cyclic cohomology and Hopf algebras. Mosh? Flato (1937--1998)   Lett. Math. Phys.   48   1   (1999)   97-108   16W30, 18G60, 19D55, 46L80, 46L85, 58B32
  • Connes, Alain   Trace formula in noncommutative geometry and the zeros of the Riemann zeta function   Selecta Math. (N.S.)   5   1   (1999)   29-106   11M26, 11R56, 58B34
  • Connes, Alain;Moscovici, H.   Hopf algebras, cyclic cohomology and the transverse index theorem   Comm. Math. Phys.   198   1   (1998)   199-246   58G12, 16W30, 19D55, 58B30
  • Connes, Alain;Kreimer, Dirk   Hopf algebras, renormalization and noncommutative geometry   Comm. Math. Phys.   199   1   (1998)   203-242   81T15, 16W30, 46L87, 81T18
  • Chamseddine, Ali H.;Connes, Alain   The spectral action principle   Comm. Math. Phys.   186   3   (1997)   731-750   58B30, 46L87, 58G40, 81T13, 81V22
  • Connes, Alain;Douglas, Michael R.;Schwarz, Albert   Noncommutative geometry and matrix theory: compactification on tori   J. High Energy Phys.     2   (1998)   35   58B30, 81T30
  • Brodzki, J.;Connes, A.;Ellwood, D.   Polarized modules and Fredholm modules   Mat. Fiz. Anal. Geom.   2   1   (1995)   15-24   58B30, 46H25, 46L05, 47B50
  • Connes, Alain   Spontaneous symmetry breaking and geometry from the spectral point of view   J. Geom. Phys.   23   3-4   (1997)   206-234   58B30, 19K56, 46L87, 58G10, 58G12, 81R40
  • Connes, Alain   Spontaneous symmetry breaking and geometry from the spectral point of view   Asterisque     241   (1997)   313-349   58B30, 19K56, 46L87, 58G10, 58G12, 81R40
  • Chamseddine, Ali H.;Connes, Alain   Universal formula for noncommutative geometry actions: unification of gravity and the standard model   Phys. Rev. Lett.   77   24   (1996)   4868-4871   58B30, 81T13, 81V17
  • Connes, Alain   Gravity coupled with matter and the foundation of non-commutative geometry   Comm. Math. Phys.   182   1   (1996)   155-176   58B30, 46L87, 81V17, 83C45
  • Connes, Alain;Damour, Thibault;Fayet, Pierre   Aspherical gravitational monopoles   Nuclear Phys. B   490   1-2   (1997)   391-431   83C99, 81T99
  • Connes, Alain;Schwarz, Albert   Matrix Vieta theorem revisited   Lett. Math. Phys.   39   4   (1997)   349-353   15A24
  • Connes, Alain   Trace formula in noncommutative geometry and the Riemann hypothesis   C. R. Acad. Sci. Paris S?r. I Math.   323   12   (1996)   1231-1236   11M26, 47B99, 58B30
  • Bost, J.-B.;Connes, A.   Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory   Selecta Math. (N.S.)   1   3   (1995)   411-457   46L35, 11M06, 11R18, 11Z05, 20G30, 82B10, 82B26
  • Connes, Alain   Geometry from the spectral point of view   Lett. Math. Phys.   34   3   (1995)   203-238   46L87, 19K56, 35S05, 46L60, 58G12
  • Connes, Alain   Noncommutative geometry and reality   J. Math. Phys.   36   11   (1995)   6194-6231   58B30, 19K35, 46L87, 58Z05, 81V22
  • Connes, A.;Moscovici, H.   The local index formula in noncommutative geometry   Geom. Funct. Anal.   5   2   (1995)   174-243   58G12, 46L87, 58B30
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   94     (1993-1994)   115-121   46L87, 46L89, 58B30
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   93     (1992-1993)   133-138   46L87, 46L89, 58B30
  • Connes, A.;Rovelli, C.   von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories   Classical Quantum Gravity   11   12   (1994)   2899-2917   82C03, 46L10, 46L60, 81P05, 82B10, 83C99
  • Connes, Alain;Sullivan, Dennis;Teleman, Nicolas   Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes   Topology   33   4   (1994)   663-681   58G12, 19D55, 30C65, 58B30
  • Connes, Alain;Moscovici, Henri   Transgression and the Chern character of finite-dimensional $K$-cycles   Comm. Math. Phys.   155   1   (1993)   103-122   46L80, 19D55, 46M20, 58G12
  • Connes, Alain;Sullivan, Dennis;Teleman, Nicolas   Local formulas for topological Pontryagin classes   C. R. Acad. Sci. Paris S?r. I Math.   317   5   (1993)   521-526   58G12, 46L80, 57N15, 58B30
  • Bost, Jean-Beno?t;Connes, Alain   Euler products and type-${rm III}$ factors   C. R. Acad. Sci. Paris S?r. I Math.   315   3   (1992)   279-284   46L55, 11M06, 46L35, 82B10
  • Connes, A.;Gromov, M.;Moscovici, H.   Group cohomology with Lipschitz control and higher signatures   Geom. Funct. Anal.   3   1   (1993)   1-78   19K56, 19E99, 46L87, 57R99, 58G12
  • Connes, Alain;Flato, Mosh?;Sternheimer, Daniel   Closed star products and cyclic cohomology   Lett. Math. Phys.   24   1   (1992)   1-12   19D55, 17B65, 19K56, 58F05, 58G15
  • Connes, A.   On the nature of mathematical reality   Elem. Math.   47   1   (1992)   19-26   00A30
  • Connes, Alain;Lott, John   Particle models and noncommutative geometry   Nuclear Phys. B Proc. Suppl.   18B     (1990)   29-47   58B30, 46L60, 46L87, 81V25
  • Connes, A.   On the Chern character of $theta$ summable Fredholm modules   Comm. Math. Phys.   139   1   (1991)   171-181   19D55, 46M20, 47N99, 57T05, 58G12
  • Connes, Alain   Characters of $theta$-summable Fredholm representations of discrete groups   C. R. Acad. Sci. Paris S?r. I Math.   312   9   (1991)   661-666   19K56, 19D55, 46L80
  • Connes, Alain;Moscovici, Henri   Cyclic cohomology, the Novikov conjecture and hyperbolic groups   Topology   29   3   (1990)   345-388   58G12, 19D55, 19K56, 46L80, 57R20
  • Connes, Alain;Higson, Nigel   Deformations, asymptotic morphisms and bivariant $K$-theory   C. R. Acad. Sci. Paris S?r. I Math.   311   2   (1990)   101-106   46L80, 19K35
  • Connes, Alain;Gromov, Mikha?l;Moscovici, Henri   The Novikov conjecture and almost flat vector bundles   C. R. Acad. Sci. Paris S?r. I Math.   310   5   (1990)   273-277   57R19, 19M05, 46L80, 46L87, 58G12
  • Connes, A.   The action functional in noncommutative geometry   Comm. Math. Phys.   117   4   (1988)   673-683   58G12, 46L87, 47B10, 47D25, 58B30, 58G15, 81T13
  • Connes, Alain;Evans, David E.   Embedding of ${rm U}(1)$-current algebras in noncommutative algebras of classical statistical mechanics   Comm. Math. Phys.   121   3   (1989)   507-525   46L60, 82A69
  • Connes, A.   Compact metric spaces, Fredholm modules, and hyperfiniteness   Ergodic Theory Dynam. Systems   9   2   (1989)   207-220   46L80, 19K56, 22D25, 58B15, 58G12
  • Connes, A.;Woods, E. J.   Hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks   Pacific J. Math.   137   2   (1999)   226-243   46L50, 28D15, 46L35, 60J15, 60J50
  • Connes, Alain;Moscovici, Henri   Hyperbolic groups and the Novikov conjecture   C. R. Acad. Sci. Paris S?r. I Math.   307   9   (1988)   475-480   57R20, 19K56, 22E40, 46L80, 58G10, 58G12
  • Connes, A.   Dixmier trace, Fredholm modules and Riemannian geometry   Nuclear Phys. B Proc. Suppl.   5B     (1988)   65-70   58B15, 17B65, 46L99, 58G12
  • Connes, Alain;Karoubi, Max   Multiplicative character of a Fredholm module   K-theory   2   3   (1988)   431-463   58G12, 16A54, 19C09, 19K33, 22E65, 46L80, 46M20, 5
  • Connes, A.   Entire cyclic cohomology of Banach algebras and characters of $theta$-summable Fredholm modules   K-theory   1   6   (1988)   519-548   46M20, 16A61, 19K56, 46H05, 46L80, 58B15, 58G12
  • Connes, A.;Cuntz, J.   Quasihomomorphisms, cyclic homology and positivity   Comm. Math. Phys.   114   3   (1988)   515-526   46L80, 19K99, 58B15, 58G12
  • Connes, A.;Narnhofer, H.;Thirring, W.   Dynamical entropy of $Csp *$ algebras and von Neumann algebras   Comm. Math. Phys.   112   4   (1987)   691-719   46L66, 58F11, 82A15
  • Connes, Alain;Moscovici, Henri   Cyclic cohomology and the transgression of the Chern character   C. R. Acad. Sci. Paris S?r. I Math.   303   18   (1986)   913-918   58B15, 18F25, 19D55, 19K56, 58A12, 58G10
  • Connes, A.   Factors of type ${rm III}sb 1$, property $Lsb lambda'$ and closure of inner automorphisms   J. Operator Theory   14   1   (1985)   189-211   46L35
  • Connes, A.   Index of subfactors, Hecke algebras and knot theory (following Vaughan Jones)   Asterisque     133-134   (1986)   289-308   46L35, 46L10, 57M25
  • Connes, Alain   Noncommutative differential geometry   Inst. Hautes ?tudes Sci. Publ. Math.     62   (1985)   257-360   58G12, 16A61, 18F25, 19D55, 19K56, 46L80, 53C99
  • Connes, A.;Skandalis, G.   The longitudinal index theorem for foliations   Publ. Res. Inst. Math. Sci.   20   6   (1984)   1139-1183   58G12, 18F25, 19K56, 46L80, 46M20, 57R30
  • Connes, Alain   Kolmogorov-Sinai entropy and quantum statistical mechanics   C. R. Acad. Sci. Paris S?r. I Math.   301   1   (1985)   1-6   46L60, 46L40, 46L50, 82A15
  • Connes, A.;Woods, E. J.   Approximately transitive flows and ITPFI factors   Ergodic Theory Dynam. Systems   5   2   (1985)   203-236   46L55, 28D99, 46L35
  • Connes, Alain;Karoubi, Max   Multiplicative character of a Fredholm module   C. R. Acad. Sci. Paris S?r. I Math.   299   19   (1984)   963-968   58B15, 18F25, 19K99, 46L80, 46M20
  • Connes, Alain   Cyclic cohomology and functors ${rm Ext}sp n$   C. R. Acad. Sci. Paris S?r. I Math.   296   23   (1983)   953-958   18F25, 19D55, 46L80
  • Connes, A.;Jones, V.   Property $T$ for von Neumann algebras   Bull. London Math. Soc.   17   1   (1985)   57-62   46L35, 22D25
  • Connes, A.;Feldman, J.;Weiss, B.   An amenable equivalence relation is generated by a single transformation   Ergodic Theory Dynam. Systems   1   4   (1981)   431-450   46L55, 22D40
  • Connes, Alain;Moscovici, Henri   The $Lsp{2}$-index theorem for homogeneous spaces of Lie groups   Ann. of Math. (2)   115   2   (1982)   291-330   58G12, 22E27, 22E45, 22E46, 43A25, 46L99, 55R50
  • Connes, A.;Jones, V.   A ${rm II}sb{1}$ factor with two nonconjugate Cartan subalgebras   Bull. Amer. Math. Soc. (N.S.)   6   2   (1982)   211-212   46L36, 46L55
  • Connes, Alain;Woods, E. J.   A construction of approximately finite-dimensional non-ITPFI factors   Canad. Math. Bull.   23   2   (1980)   227-230   46L55, 46L10
  • Connes, A.   An analogue of the Thom isomorphism for crossed products of a $Csp{*} $-algebra by an action of $R$   Adv. In Math.   39   1   (1981)   31-55   46L55, 46M20, 55N15, 58G15
  • Connes, Alain;Skandalis, Georges   Th?or?me de l'indice pour les feuilletages   C. R. Acad. Sci. Paris S?r. I Math.   292   18   (1981)   871-876   58G12, 57R30
  • Connes, A.;Weiss, B.   Property ${rm T}$ and asymptotically invariant sequences   Israel J. Math.   37   3   (1980)   209-210   28D15, 22D40
  • Connes, Alain;Takesaki, Masamichi   "Errata: ""The flow of weights on factors of type ${rm III}$"""   Tohoku Math. J.   30   4   (1978)   653-655   46L10, 46L35, 46L55
  • Connes, A.   On the spatial theory of von Neumann algebras   J. Funct. Anal.   35   2   (1980)   153-164   46L10, 46L40
  • Connes, Alain   $Csp{*} $ alg?bres et g?om?trie diff?rentielle   C. R. Acad. Sci. Paris S?r. A-B   290   12   (1980)   A599-A604   46L55, 53C05, 58G12
  • Connes, A.   A factor of type ${rm II}sb{1}$ with countable fundamental group   J. Operator Theory   4   1   (1980)   151-153   46L10, 22D35
  • Connes, Alain;Moscovici, Henri   The $Lsp{2}$-index theorem for homogeneous spaces   Bull. Amer. Math. Soc. (N.S.)   1   4   (1979)   688-690   58G10, 22E45
  • Connes, A.   On the cohomology of operator algebras   J. Functional Analysis   28   2   (1978)   248-253   46L10
  • Connes, Alain;Størmer, Erling   Homogeneity of the state space of factors of type ${rm III}sb{1}$   J. Functional Analysis   28   2   (1978)   187-196   46L10
  • Connes, A.   Classification of injective factors. Cases $IIsb{1},$ $IIsb{infty },$ $IIIsb{lambda },$ $lambda not=1$   Ann. of Math. (2)   104   1   (1976)   73-115   46L10
  • Connes, A.;Størmer, E.   Entropy for automorphisms of $IIsb{1}$ von Neumann algebras   Acta Math.   134   3-4   (1975)   289-306   46L10
  • Connes, A.   Periodic automorphisms of the hyperfinite factor of type II1   Acta Sci. Math. (Szeged)   39   1-2   (1977)   39-66   46L10
  • Connes, Alain;Krieger, Wolfgang   Measure space automorphisms, the normalizers of their full groups, and approximate finiteness   J. Functional Analysis   24   4   (1977)   336-352   28A65
  • Connes, A.   A factor not anti-isomorphic to itself   Bull. London Math. Soc.   7     (1975)   171-174   46L10
  • Connes, A.   On the hierarchy of W. Krieger   llinois J. Math.   19     (1975)   428-432   46L10, 28A65
  • Connes, Alain   Outer conjugacy classes of automorphisms of factors   Ann. Sci. ?cole Norm. Sup. (4)   8   3   (1975)   383-419   46L10
  • Connes, A.   Classification of automorphisms of hyperfinite factors of type ${rm II}sb{1}$ and ${rm II}sb{infty }$ and application to type ${rm III}$ factors   Bull. Amer. Math. Soc.   81   6   (1975)   1090-1092   46L10
  • Connes, Alain   Sur la classification des facteurs de type ${rm II}$   C. R. Acad. Sci. Paris S?r. A-B   281   1   (1975)   A13-A15   46L10
  • Connes, Alain   Caract?risation des espaces vectoriels ordonn?s sous-jacents aux alg?bres de von Neumann   Ann. Inst. Fourier (Grenoble)   24   4   (1974)   121-155   46L10
  • Connes, A.   On hyperfinite factors of type ${rm III}sb{0}$ and Krieger's factors   J. Functional Analysis   18     (1975)   318-327   46L10
  • Connes, A.   A factor not anti-isomorphic to itself   Ann. of Math. (2)   101     (1975)   536-554   46L10
  • Connes, Alain;Woods, Edward James   Existence de facteurs infinis asymtotiquement ab?liens   C. R. Acad. Sci. Paris S?r. A   279     (1974)   189-191   46L10
  • Connes, Alain   Sur le th?or?me de Radon-Nikodym pour les poids normaux fid?les semi-finis   Bull. Sci. Math. (2)   97     (1973)   253-258   46L10
  • Connes, A.   Almost periodic states and factors of type ${rm III}sb{1}$   J. Functional Analysis   16     (1974)   415-445   46L10
  • Connes, Alain;Takesaki, M.   Flots des poids sur les facteurs de type ${rm III}$   C. R. Acad. Sci. Paris S?r. A   278     (1974)   945-948   46L10
  • Connes, Alain   Une classification des facteurs de type ${rm III}$   Ann. Sci. ?cole Norm. Sup. (4)   6     (1973)   133-252   46L10
  • Connes, Alain;van Daele, Alfons   The group property of the invariant $S$ of von Neumann algebras   Math. Scand.   32     (1973)   187-192   46L10
  • Connes, Alain   Une classification des facteurs de type ${rm III}$   C. R. Acad. Sci. Paris S?r. A-B   275     (1972)   A523-A525   46L10
  • Connes, Alain   Groupe modulaire d'une alg?bre de von Neumann   C. R. Acad. Sci. Paris S?r. A-B   274     (1972)   A1923-A1926   46L10
  • Connes, Alain   ?tats presque p?riodiques sur une alg?bre de von Neumann   C. R. Acad. Sci. Paris S?r. A-B   274     (1972)   A1402-A1405   46L10
  • Connes, Alain   Calcul des deux invariants d'Araki et Woods par la th?orie de Tomita et Takesaki   C. R. Acad. Sci. Paris S?r. A-B   274     (1972)   A175-A177   46L10
  • Connes, Alain   Un nouvel invariant pour les alg?bres de von Neumann   C. R. Acad. Sci. Paris S?r. A-B   273     (1971)   A900-A903   46.65
  • Connes, Alain   D?termination de mod?les minimaux en analyse non standard et application   C. R. Acad. Sci. Paris S?r. A-B   271     (1970)   A969-A971   02.57
  • Connes, Alain   Ordres faibles et localisation des z?ros de polynomes   C. R. Acad. Sci. Paris S?r. A-B   269     (1969)   A373-A376   12.70
  • Connes, Alain   Sur une g?n?ralisation de la notion de corps ordonn?   C. R. Acad. Sci. Paris S?r. A-B   269     (1969)   A337-A340   12.70
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   92     (1991-1992)   135-142   46L60, 46N55, 82C05, 82C10
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   91     (1990-1991)   139-145   46L87
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   90     (1989-1990)   105-108   46L87, 81V22
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   89     (1988-1989)   97-104   57Rxx, 19D55, 58G12
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   88     (1987-1988)   103-110   46L87
  • Connes, Alain   Analysis and geometry   Ann. Coll?ge France   87     (1986-1987)   99-104   46L80, 46H25, 46M20
  • Connes, Alain   Geometric interpretation of the standard model of particle physics and fine structure of space-time   C. R. Acad. Sci. Paris S?r. A-B   10   3   (1993)   223-234   81V05, 46L87, 58B30, 81-01
  • Connes, Alain;Flato, Mosh?;Hironaka, Heisuke;Jaffe, Arthur;Jones, Vaughan   Editorial (dedication of this issue to Huzihiro Araki)   Comm. Math. Phys.   155   1   (1993)   1-2   01A70
  • Kon, A.   Abstract concepts and numerical quantities   Fiz.-Mat. Spis. Bcdprime lgar. Akad. Nauk.   31   4   (1989)   301-311   00A05