Maxim Kontsevich i matematyka współczesna

• Autorzy: Żołądek H.
• Języki publikacji: PL

Słowa kluczowe

PL

Kontsevich Maxim; układ dynamiczny; grawitacja kwantowa; przestrzeń moduli; teoria strun; operady

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
• Rocznik: 2002
• Tom: [Z] 38
• Strony: 1--35
• Opis fizyczny: Bibliogr. 57 poz., rys.

Twórcy

autor

Żołądek H.

• Warszawa

Bibliografia

• [Arl] V. I. Arnold, Teoria równań różniczkowych, PWN, Warszawa, 1982.
• [Ar2] V. I. Arnold, The Vassiliev theory of discriminants and knots, w: „First European Congress of Mathematics”, tom I, Progress in Math. 120, Birkhäuser, Basel, 1994, 3-29.
• [AsMo] P. A. Aspinwall, D. R. Morrison, Topological field theory and rational curves, Comm. Math. Phys. 151 (1993), 245-262.
• [At] M. Atiyah, The geometry and physics of knots, Cambridge University Press, Cambridge, 1990.
• [BaKo] S. Barannikov, M. Kontsevich, Frobenius manifolds and formality of Lie algebra of polyvector fields, Internat. Math. Res. Notices (1998), no. 1, 201-215.
• [Ba] D. Bar-Nathan, On the Vassiliev knot invariants, Topology 34 (1995), 423-472.
• [BFFLS] F. Bayen, M. Flato, C. Frønsdal, A. Lichnerowicz, D. Sternheimer, Deformation theory and quantization I. Deformation of symplectic structures, Ann. Phys. 111 (1978), no. 1, 61-110.
• [BIZ] D. Bessis, C. Itzykson, J. B. Zuber, Quantum field theory techniques in graphical enumeration, Adv. Appl. Mat. 1 (1980), 109-157.
• [COGP] P. Candelas, X. de la Ossa, P. S. Green, L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991), 21-74; oraz w: „Essays on mirror symmetry” (S.-T. Yau, ed.), International Press, Hong Kong, 1992, 31-95; oraz w: AMS/IP Studies in Adv. Math. 9 (1998), 31-95.
• [CoKa] D. A. Cox, S. Katz, Mirror symmetry and algebraic geometry, Math. Surveys Monogr. 68, Amer. Math. Soc., Providence, 1998.
• [D’H] E. D’Hoker, String theory, w: „Quantum fields and strings. A course for mathematicians”, tom II (P. Deligne and others, eds.), Amer. Math. Soc., Providence, 1999, 807-1011.
• [DiIt] P. Di Francesco, C. Itzykson, Quantum intersection rings, w: „Moduli of algebraic curves (Texel Island, 1994)” (H. Dijkgraaf and G. van der Geer, eds.), Birkhäuser, Boston, 1995, 81-148.
• [Du] B. Dubгоvin, Geometry of 2D topological field theories, w: „Integrable systems and quantun groups” (M. Francaviglia and S. Greco, eds.), Lecture Notes in Math. 1620, Springer, 1996, 20-348.
• [DuKw] B. Duplantier, K.-H. Кwоn, Conformal invariance and intersection of random walks, Phys. Rev. Lett. 61 (1988), 2514-2517.
• [ElSt] G. Ellingsgrund, S. Strømme, The number of twisted cubics on the general quintic threefold, Math. Scand. 76 (1995), 5-34.
• [FuOn] K. Fukaya, K. Ono, Arnold Conjecture and Gromov-Witten invariants, Topology 38 (1999), no. 5, 933-1048.
• [Gi] A. B. Givental, Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices 13 (1996), 613-663.
• [Gr] M. Gromov, Pseudo-holomorpic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
• [KKR] M. Ya. Kel’bert, M. L. Kontsevich, A. N. Ryabko, Jackson networks on countable graphs, Theory Probab. Appl. 33 (1988) no. 2, 358-361 (1989); po rosyjsku: Teor. Veroyatnost. i Primenen. 33 (1988) no. 2, 379-382.
• [KiKo] A. A. Kirillov, M. L. Kontsevich, The growth of the Lie algebra generated by two generic vector fields on the line, Vestnik Moscov Univ. Ser. I Mat. Mekh. (1983), no. 4, 15-20 (po rosyjsku).
• [Ko1] M. L. Kontsevich, The Virasoro algebra and Teichmüller spaces, Funktsional. Anal. i Prilozhen. 21 (1987), no. 2, 78-79 (po rosyjsku).
• [Ko2] M. L. Kontsevich, Intersection theory on the moduli space of curves, Funct. Anal. Appl. 25 (1991), no. 2, 123-129; po rosyjsku: Funktsional. Anal. i Prilozhen. 25 (1991) no. 2, 50-57.
• [Ko3] M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992), no. 1, 1-23.
• [Ko4] M. Kontsevich, Formal (non)commutative symplectic geometry, w: „The Gelfand Mathematical Seminars 1990-1992”, Birkhäuser, Boston, 1993,173-187.
• [Ko5] M. Kontsevich, Vassiliev’s knot invariants, w: „I. M. Gelfand Seminar”, Adv. Soviet Math. 16, Part 2, Amer. Math. Soc., Providence, 1993, 137-150.
• [Ко6] M. Kontsevich, Feynman diagrams and low-dimensional topology, w: „First European Congress of Mathematics (Paris 1992)”, tom II, Progress in Math. 120, Birkhäuser, Basel, 1994, 97-121.
• [Ko7] M. Kontsevich, Enumeration of rational curves via torus action, w: „Moduli of algebraic curves (Texel Island, 1994)” (H. Dijkgraaf and G. van der Geer, eds.), Birkhäuser, Boston, 1995, 335-368.
• [Ko8] M. Kontsevich, Homological algebra of mirror symmetry, w: „Proceedings of the ICM (Zurich, 1994)”, Birkhäuser, Basel, 1995, 120-139.
• [Ko9] M. Kontsevich, Mirror symmetry in dimension 3, Séminaire Bourbaki 1994/95, Astérisque 237 (1996), Exp. No. 801, 275-293.
• [Ko10] M. Kontsevich, Lyapunov exponents and Hodge theory, w: „The mathematical beauty of physics (Saclay 1996)”, Adv. Ser. Math. Phys., 24, World Sci. Publ., River Edge, 1997, 318-332.
• [Ko11] M. Kontsevich, Product formulas for modular forms on 0 (2, n) (after R. Borcherds), Séminaire Bourbaki 1996/97, Astérisque 245 (1997), Exp. No. 821, 41-56.
• [Ko12] М. Kontsevich Deformation quantization of Poisson manifolds. I, preprint, 1997, http://xxx.lanl.gov/abs/q-alg/9709040.
• [Ko13] M. Kontsevich, Rozansky-Witten invariants via formal geometry, Compositio Math. 115 (1999), no. 1, 115-127.
• [Ko14] M. Kontsevich, Operads and motives in deformation quantization. Moshé Flato (1937-1998), Lett. Math. Phys. 48 (1999), no. 1, 35-72.
• [Ko15] M. Kontsevich, The 1½-logarithm, Appendix w: P. Ebaz-Vincent and H. Gangl, „On poly(ana)logs I”, preprint, 2001.
• [KM1] M. Kontsevich, Yu. Manin, Gromov-Witten classes, quantum cohomology and enumerative geometry, Comm. Math. Phys. 164 (1994), no. 3, 525-562.
• [KМ2] M. Kontsevich, Yu. Manin, Quantum cohomology of a product, Invent. Math. 124 (1996), no. 1-3, 313-339.
• [KM3] M. Kontsevich, Yu. Manin, Relations between the correlators of the topological sigma-model coupled to gravity, Comm. Math. Phys. 196 (1998), no. 2, 385-398.
• [KoRo] M. Kontsevich, A. L. Rosenberg, Noncommutative smooth spaces, w: „The Gelfand Mathematical Seminars, 1996-1999”, Birkhäuser, Boston, 2000, 85-108.
• [KoSo] M. Kontsevich, Y. Soibelman, Deformations of algebras over operads and the Deligne conjecture, w: „Conférence Moshé Flato (Dijon 1999)”, tom I, Math. Phys. Stud. 21, Kluwer Acad. Publ., Dordrecht, 2000, 255-307.
• [KoSu] M. L. Kontsevich, Yu. M. Suhov, Statistics of Klein polyhedra and multidimensional continued fractions, w: „Pseudoperiodic topology”, Amer. Math. Soc. Transl. Ser. 2, 197, Amer. Math. Soc., Providence, 1999, 9-27.
• [KoVi] M. Kontsevich, S. Vishik, Geometry of determinants of elliptic operators, w: „Functional Analysis on the eve of the 21st century (New Brunswick, 1993)”, Progr. Math. 131, Birkhäuser, Boston, 1995, 173-197.
• [KoZa] M. Kontsevich, D. Zagier, Periods, w: „Mathematics unlimited – 2001 and beyond”, Springer, Berlin, 2001, 771-808.
• [LSW] G. F. Lawler, O. Schramm, W. Werner, Values of Brownian intersection exponents, II. Plane exponents, Acta Math. 187 (2001), 275-308.
• [LLMM] J. Lepovsky, J. Lindenstrauss, Yu. I. Manin, J. Milnor, The mathematical work of the 1998 Fields medalists, Notices Amer. Math. Soc. 46 (1999), no. 1, 17-26.
• [Lo] E. Loijenga, Motivic measures, Séminaire Bourbaki 1999-2000 (2000), Exp. No. 874, 1-28.
• [MJD] T. Miwa, M. Jimbo, E. Date, Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras, Cambridge University Press, Cambridge, 2000.
• [SeWi] G. Segal, G. Wilson, Loop groups and equations of KdV type, Publ. Math. IHES 61 (1985), 5-65; także po rosyjsku w: E. Presli, G. Sigal, „Grupy petel”, Mir, Moskwa, 1990, 379-442.
• [St] A. Strominger, Kaluza-Klein compactifications, supersymmetry and Calabi-Yau spaces, w: „Quantum fields and strings. A course for mathematicians”, v. II (P. Deligne and others, eds.), Amer. Math. Soc., Providence, 1999, 1091-1115.
• [Ta] C. H. Taubes, The work of Maxim Kontsevich, w: „Proceedings of the International Congress of Mathematicians, tom I (Berlin, 1998)”, Doc. Math. 1998, 119-126.
• [Vo] C. Voisin, Symmétrie mirroir, Panoramas et synthèses 2, Soc. Math. France, Paris, 1996; po angielsku: Mirror symmetry, SMF/AMS Texts and Monographs 1, Amer. Math. Soc., Providence, 1999.
• [We] S. Weinberg, Teoria pól kwantowych. Nowoczesne zastosowania, PWN, Warszawa, 1999.
• [Wi1] E. Witten, Some applications of quantum field theory, w: „IXth International Congress on Mathematical Physics (Swansea 1988)”, IOP Publishing Ltd, 1989, 77-116.
• [Wi2] E. Witten, Two dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geom. 1 (1991), 243-310.
• [Wi3] E. Witten, Mirror manifolds and topological field theory, w: „Essays on mirror symmetry” (S.-T. Yau, ed.), International Press, Hong Kong, 1992, 121-159; oraz w: AMS/IP Studies in Adv. Math. 9 (1998), 121-159.
• [Za] D. Zagier, Values of zeta functions and their applications, w: „First European Congress of Mathematics (Paris 1992)”, tom II, Progr. Math. 120, Birkhäuser, Basel, 1994, 497-512.
• [ZMNP] V. E. Zakharov, S. V. Manаkоv, S. P. Novikov, L. P. Pitaevskij, Teoria solitonov. Metod obratnoj zadači, Nauka, Moskwa, 1980 (po rosyjsku); po angielsku: Theory of solitons. The inverse scattering method, Contemporary Sov. Math., Consultants Bureau, New York, 1984.