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André, Yves:
Ambiguity Theory, Old and New
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.1, p. 259-274, (English)
pdf (278 Kb), djvu (164 Kb). | MR 2493655 | Zbl 1189.11050

Sunto

This is an introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.
Referenze Bibliografiche
[1] ANDRÉ YVES, Une introduction aux motifs (motifs purs, motifs mixtes, périodes). Panoramas et Synthèses 17. Société Mathématique de France, Paris, 2004. | MR 2115000 | Zbl 1060.14001
[2] ANDRÉ YVES, Galois theory, motives, and transcendental number theory, submitted. | fulltext (doi) | MR 2588609 | Zbl 1219.11109
[3] BELKALE PRAKASH - BROSNAN PATRICK, Periods and Igusa local zeta functions, International Mathematics Research Notices. Vol. 2003, no. 49 (2003), 2655-2670. | fulltext (doi) | MR 2012522 | Zbl 1067.11075
[4] BLOCH SPENCER - ESNAULT HÉLÈNE - KREIMER DIRK, On motives associated to graph polynomials, Comm. Math. Phys., 267, no. 1 (2006), 181-225. | fulltext (doi) | MR 2238909 | Zbl 1109.81059
[5] CARTIER PIERRE, A mad day's work: from Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry [in Les relations entre les mathématiques et la physique théorique, 23-42, Inst. Hautes Âetudes Sci., Bures-sur-Yvette, 1998; Translated from the French by Roger Cooke. Bull. Amer. Math. Soc. (N.S.) 38, no. 4 (2001), 389-408 (electronic). | fulltext EuDML | fulltext (doi) | MR 1848254
[6] CASALE GUY, Le groupoïde de Galois de P1 et son irréductibilité, to appear in Commentarii Mathematici Helvetici. | fulltext (doi) | MR 2410777
[7] CONNES ALAIN, Renormalisation et ambiguïté galoisienne. Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. I. Astérisque No. 296 (2004), 113-143. | MR 2135686
[8] CONNES ALAIN - MARCOLLI MATILDE, Noncommutative geometry, quantum fields and motives. American Mathematical Society Colloquium Publications, 55. American Mathematical Society, Providence, RI; Hindustan Book Agency, New Delhi, 2008. | MR 2371808 | Zbl 1159.58004
[9] CONNES ALAIN - MARCOLLI MATILDE, Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory. Frontiers in number theory, physics, and geometry. II (Springer, Berlin, 2007), 617-713. | fulltext (doi) | MR 2290770 | Zbl 1200.81113
[10] 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, no. 1 (2000), 249-273. | fulltext (doi) | MR 1748177 | Zbl 1032.81026
[11] DELIGNE PIERRE - GONCHAROV ALEXANDER, Groupes fondamentaux motiviques de Tate mixte. Ann. Sci. École Norm. Sup. (4) 38, no. 1 (2005), 1-56. | fulltext EuDML | fulltext (doi) | MR 2136480 | Zbl 1084.14024
[12] EHRHARDT CAROLINE, Evariste Galois et la théorie des groupes. Fortune et réélaborations (1811-1910), thèse ENS (2007). | MR 2537664
[13] FURUSHO HIDEKAZU, Pentagon and hexagon equations, arXiv:math/0702128. | fulltext (doi) | MR 2630048 | Zbl 1257.17019
[14] GALOIS EVARISTE, Œuvres mathématiques, Gauthiers-Villars, 1951.
[15] GRAY JEREMY, Linear differential equations and group theory from Riemann to Poincaré. Second edition. Birkhäuser Boston, Inc., Boston, MA, 2000. | MR 1751835 | Zbl 0949.01001
[16] GROTHENDIECK ALEXANDRE, Esquisse d'un programme. With an English translation on pp. 243-283. London Math. Soc. Lecture Note Ser., 242, Geometric Galois actions, 1, 5-48, Cambridge Univ. Press, Cambridge, 1997. | MR 1483107
[17] JORDAN CAMILLE, Mémoire sur les équations différentielles linéaires à intégrale algébrique (1878), Oeuvres II, 13-140.
[18] KATZ NICHOLAS, web page: http://www.monodromy.com/ | MR 2183396
[19] KONTSEVICH MAXIM - ZAGIER DON, Periods. Mathematics unlimited-2001 and beyond (Springer, Berlin, 2001), 771-808. | MR 1852188
[20] LANG SERGE, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. (1966). | MR 214547 | Zbl 0144.04101
[21] LAUTMAN ALBERT, Essai sur les notions de structure et d'existence en mathématiques. Reprint, Vrin 2006. | fulltext (doi) | MR 3775305
[22] LOCHAK PIERRE - SCHNEPS LEILA, Open problems in Grothendieck-Teichmller theory. Problems on mapping class groups and related topics, 165-186, Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI, 2006. | fulltext (doi) | MR 2264540 | Zbl 1222.14046
[23] MALGRANGE BERNARD, On nonlinear differential Galois theory. Frontiers in mathematical analysis and numerical methods, 185-196, World Sci. Publ., River Edge, NJ, 2004. | MR 2172556
[24] MORALES-RUIZ JUAN - RAMIS JEAN PIERRE, Galoisian obstructions to integrability of Hamiltonian systems. I, II. Methods Appl. Anal., 8, no. 1 (2001), 33-95, 97-111. | fulltext (doi) | MR 1867495 | Zbl 1140.37352
[25] PICARD EMILE, La vie et l'oeuvre de Joseph Boussinesq, Discours et Notices, Gauthiers-Villars (1936).
[26] VAN DER PUT MARIUS - SINGER MICHAEL, Galois theory of linear differential equations, Springer Grundlehren der math. Wiss. 328 (2003). | fulltext (doi) | MR 1960772 | Zbl 1036.12008
[27] RIEMANN BERNHARD, Beiträge zur Theorie der durch die Gauss'sche Reihe $F(\alpha, \beta, \gamma, x)$ darstellbaren Funktionen, Abh. Kon. Ges. Wiss. Gottingen, VII Math. Classe A-22 (1857). | fulltext EuDML
[28] SCHLESINGER LUDWIG, Handbuch der Theorie der linearen Differentialgleichungen. In zwei Banden. Band II: Theil 1, (Schluss-) Theil 2. (German) Reprint. Bibliotheca Mathematica Teubneriana, Band 31 Johnson Reprint Corp., New York-London 1968. | fulltext EuDML | MR 252187
[29] H. A. SCHWARZ, Über diejenigen Fälle, in welchen die Gaussische hypergeometrische Reihe eine algebraische Funktion ihres vierten Elements darstellt, J. Reine Angew. Math., 75 (1872), 292-335. | fulltext EuDML | fulltext (doi) | MR 1579568 | Zbl 05.0146.03
[30] UMEMURA HIROSHI, Lie-Drach-Vessiot theory-infinite-dimensional differential Galois theory. CR-geometry and overdetermined systems (Osaka, 1994), 364-385, Adv. Stud. Pure Math., 25, Math. Soc. Japan, Tokyo, 1997. | MR 1476252
[31] WEIL ANDRÉ, De la métaphysique aux mathématiques (1960), Oeuvres, vol. II, Springer, 408-412.
[32] Singularités irrégulières - Correspondance et documents, Pierre Deligne - Bernard Malgrange - Jean-Pierre Ramis, Documents Mathématiques 5 (2007), SMF. | MR 2387754

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