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Maxim Kontsevich - List of published works#


  • Symplectic geometry of homological algebra - pictures
  • Generalized Tian-Todorov theorems, talk on Kinosaki conference 2008
  • Holonomic D-modules and positive characteristic, Japan. J. Math. 4, 1-25 (2009).
  • Stability structures, motivic Donaldson-Thomas invariants and cluster transformations (with Y. Soibelman),
  • Hodge theoretic aspects of mirror symmetry (with L. Katzarkov and T. Pantev), Proceedings of Symposia in Pure Mathematics vol. 78 (2008), "From Hodge theory to integrability and TQFT: tt*-geometry", eds. Ron Y. Donagi and Katrin Wendland, 87-174,
  • XI Solomon Lefschetz Memorial Lecture Series: Hodge structures in non-commutative geometry.(Notes by Ernesto Lupercio), Contemp. Math. vol. 462 (2008), 1-21, e-print 0801.4760.
  • Motivic Donaldson-Thomas invariants, talk on Arbeitstagung 2007
  • Notes on motives in finite characteristic, to appear in "Manin's Festschrift" ed. Yu. Zarkhin and Yu. Tschinkel,
  • On Malliavin measures, SLE and CFT (with Yu. Suhov), Proceedings of the Steklov Institute of Mathematics, vol. 258 (2007), pages 100-146
  • Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I (with Y. Soibelman), in "Homological Mirror Symmetry: New Deevelopments and Perspectives" (A.Kapustin et al. (Eds.)), Lect. Notes in Physics 757 (Springer, Berlin Heidelberg 2009) 153-219.
  • Integrality of instanton numbers and p-adic B-model (with A.Schwarz and V.Vologodsky),Phys. Lett. B637 (2006), 97-101.
  • Hochschild and Harrison cohomology of complete intersections, Appendix to Quantization on Curves by Chris Fronsdal, Lett. Math. Physics. 79(2007), no.2,124--129. e-print math-ph/0507021.
  • Automorphisms of the Weyl algebra (with A. Belov-Kanel), Lett. Math. Phys., vol.74(2005), No. 2, 181-199.
  • The Jacobian Conjecture is stably equivalent to the Dixmier Conjecture (with A. Belov-Kanel), Moscow Mathematical Journal, 7 (2007), no.2, 209-218.
  • Symmetries of WDVV equations (with Y.Chen and A.Schwarz), Nucl. Phys. B730 (2005), 352-363.
  • Affine structures and non-archimedean analytic spaces (with Y. Soibelman), in "The Unity of Mathematics" in honor of the 90-th anniversary of I.M.Gelfand, Progress in Mathematics Volume 244, Birkhauser, 2005, 312-385.
  • CFT, SLE and phase boundaries, talk on Arbeitstagung 2003,
  • Connected components of the moduli spaces of Abelian differentials with prescribed singularities (with A.Zorich), Invent. Math. 153 (2003), 631-678.
  • Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), 157-216.
  • Deformation quantization of algebraic varieties, Lett. Math. Physics. 56 (2001), 271-294.
  • Homological mirror symmetry and torus fibrations (with Y.Soibelman), in "Symplectic Geometry and Mirror Symmetry", Proceedings of 4th KIAS conference, Eds. K.Fukaya, Y.-G.Oh, K.Ono and G.Tian, World Scientific, 2001.
  • Periods (with D.Zagier) , in "Mathematics Unlimited, Year 2001 and Beyond", Eds. B.Engquist and W.Scmidt, Springer, 2001.
  • The 1+1/2 logarithm, Appendix to On Poly(ana)logs I by Philippe Elbaz-Vincent, Herbert Gangl, Comp. Mth. 130 (2002), 211-214. e-print math.KT/0008089.
  • Deformations of algebras over operads and Deligne's conjecture (with Y.Soibelman), in "Conference Moshe Flato 1999, Quantization, Deformations, and Symmetries", vol. I, Ed. G. Dito and D. Sternheimer, Kluwer Academic Publishers, 2000, 255-307, e-print math.QA/0001151.
  • Noncommutative smooth spaces (with A.Rosenberg), in "The Gelfand Gelfand Seminars 1996-1999", ed. I.M.Gelfand, V.S.Retakh, Birkhauser 2000, 85-108.
  • Operads and Motives in Deformation Quantization, Lett. Math. Phys. 48 (1999), 35-72, e-print math.QA/9904055.
  • Rozansky-Witten classes via formal geometry, Compositio Mathematica, 115 (1999), 115-127.
  • Statistics of Klein polyhedra and multidimensional continued fractions (with Yu.Suhov), in collection "Pseudoperiodic topology", ed. V.Arnold, M.Kontsevich, A.Zorich. Amer. Math.Soc. Transl., Ser.2, vol. 197 (1999), 9-28.
  • Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields, (with S.Barannikov), Int. Math. Res. Notices 4 (1998), 201-215.
  • Relations between the correlators of the topological sigma-model coupled to gravity (with Yu.Manin), Commun.Math.Phys. 196 (1998) 385-398.
  • Formality conjecture, in "Deformation Theory and Symplectic Geometry", Proceedings of the Ascona Meeting, June 1996, ed. D.Sternheimer, J.Rawnsley and S.Gutt, Kluwer Academic Publishers 1997, 139-156.
  • Lyapunov exponents and Hodge structures, in "The mathematical beauty of physics: in memory of Claude Itzykson: Saclay, 5-7 June 1996", edited by J.M.Drouffe and J.B.Zuber,Advanced series in mathematical physics: vol. 24, World Scientific 1997, 318-332.
  • The Geometry of the Master Equation and Topological Quantum Field Theory (with M.Alexandrov, A.Schwarz and O.Zaboronsky), Intern. Jour. of Modern Phys. A, Vol. 12, No. 7 (1997), 1405-1429.
  • Quantum Cohomology of a Product (with Yu.Manin and R.Kaufmann). Invent.Math. 124, 313-339 (1996).
  • Product formulas for modular forms on O(2,n) (after R.Borcherds), Seminar N. Bourbaki, Novembre 1996, Expose 821.
  • Mirror symmetry in dimension 3, Seminar N. Bourbaki, Juin 1995, Expose 801.
  • Rigorous results in the topological sigma-model, XIth International Congress of Mathematical Physics, Paris 1994, Editor D. Iagolnitzer, International Press Inc. 1995, 47-59.
  • Homological algebra of Mirror Symmetry, Proceedings of the International Congress of Mathematicians, Zuerich 1994, vol. I, Birkhauser 1995, 120-139.
  • Enumeration of rational curves via torus actions, The Moduli Space of Curves, edited by R.Dijkgraaf, C.Faber and G. Van der Geer, Progress in Mathematics 129, Birkhauser 1995, 335-368, e-print hep-th/9405035.
  • Gromov-Witten classes, quantum cohomology, and enumerative geometry, (with Yu.Manin), Comm.Math.Phys.,164:3 (1994), 525-562, and Mirror Symmetry II, B.Greene and S.-T.Yau (editors), 1997. AMS and International Press, 607-654.
  • Geometry of Determinants of Elliptic Operators (with S.Vishik), Functional Analysis on the Eve of the 21-st Century, vol. I, Ed. S.Gindikin, J.Lepowsky, R.Wilson, Progress in Mathematics 131, Birkhauser 1995, 173-197.
  • Determinants of elliptic pseudo-differential operators (with S.Vishik), preprints IHES/M/94/30 and MPI/94-30, e-print hep-th/9404046.
  • Feynman diagrams and low-dimensional topology, First European Congress of Mathematics, 1992, Paris, Volume II, Progress in Mathematics 120, Birkhauser 1994, 97-121.
  • $A_{\infty}$-algebras in Mirror Symmetry, in 1. Mathematische Arbeitstagung (Neue Serie), Bonn 1993, preprint MPI/93-57.
  • Formal (non)-commutative symplectic geometry, The Gelfand Mathematical. Seminars, 1990-1992, Ed. L.Corwin, I.Gelfand, J.Lepowsky, Birkhauser 1993, 173-187.
  • Vassiliev's knot invariants, Adv.Soviet Math.,vol.16,Part 2(1993),137-150.
  • Intersection theory on the moduli spaces of curves and the matrix. Airy function, Comm.Math.Phys.,vol.147(1992),1-23.
  • Intersection theory on the moduli spaces of curves, Functional.Anal.Appl.,25:2(1991).
  • Rational Conformal Field Theory and Invariants of 3-dimensional Manifolds.
  • Virasoro algebra and Teichmueller spaces, Functional Anal.Appl., 21:2(1987),156-158.
  • Algebras of Intermediate Growth (with A.A.Kirillov and A.I.Molev), Selecta Mathematica Sovietica,vol.9,No.2(1990),137-153.
  • Growth of the Lie algebra generated by two vector fields on the line (with A.A.Kirillov), Moscow Univ.Math.Bull.,no.4(1983),14-20.
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