Publications of Alexandre Varchenko

Current information as of August 1997

  1. "Monodromy of Multiple Integrals Depending on Parameters," Funktsional'nyi Analiz i ego Prilozheniya 3:4 (1969), 79-80.

  2. "Theorem on Equisingularity of Families of Algebraic Manifolds," Uspekhi Matematicheskykh Nauk 26:1 (1971), 217-218.

  3. "On the Germs of Analytic Maps with Finitely Determined Topological Type," Funktsional'nyi Analiz i ego Prilozheniya 6:3 (1971), 63-64.

  4. "Theorems of Topological Equsingularity of Families of Algebraic Manifold and Polynomial Mappings," Izc. Acad. Sci. USSR 36 (1972), 957-1019.

  5. "On the Relation Between Topological and Algebro-Geometrical Equisingularities of Zarisky," Funktsional'nyi Analiz i ego Prilozheniya 7:2 (1973), 1-5.

  6. "Local Topological Properties of Analytic Mappings," IZv. Acad. Sci. USSR 37:4 (1973), 883-916.

  7. "On the Germs of Smooth Maps with Finitely Determined Topological Type," Uspekhi Matematicheskykh Nauk 28:3 (1973), 175-176.

  8. "Local Topological Properties of Smooth Mappings," Izv. Acad. Sci. USSR 38 (1974), 1037-1090.

  9. "Versal Topological Deformations," Izv. Acad. Sci. USSR 39 (1975), 294-314.

  10. "Algebro-Geometrical Equisingularity and Local Topological Classification of Smooth Mappings," Proc. Int. Cong. Math. Vancouver 1 (1975), 427-431.

  11. "Newton Polyhedra and Estimations of Oscillatory Integrals," Funktsional'nyi Analiz i ego Prilozheniya 10:3 (1976), 13-38; Functional Analysis and its Applications (Eng.Transl. of FAP) 10 (1976), 175-196.

  12. "A Zeta-Function for Monodromy and Newton Diagrams," Invent. Math. 37 (1976), 253-262.

  13. "Characteristic Polynomial of Monodromy Operator and Newton Diagram," Uspekhi Matematicheskykh Nauk 32:2 (1977), 63-64.

  14. "Applying the Method of Stationary Phase to Limit Theorems for Markov Chains," Dokl, Akad. Nauk USSR 233 (1977), 11-14; Soviet Math. Doklady 18 (1977), 10-13.

  15. "The Integrality of the Limit of the Curvature Integral Over the Boundary of an Isolated Singularity of a Surface in 3, Uspekhi Matematicheskykh Nauk 33:6 91978), 199-200.

  16. "A Formular for the Ranks of the Homology Groups of the Boundary of an Isolated Singularity of a Surface in 3 and the Newton Diagram," Funktsional'nyi Analiz i ego Prilozheniya 13:1 (1979), 64-65; Functional Analysis and its Applications (Eng. Transl. of FAP) 13 (1979), 52-53.

  17. "Contact Structures and Isolated Singularities," Vestnik MGU Ser. Mat. 2 (1980), 18-21.

  18. "The Gauss-Manin Connection and the Bernstein Polynomial," Uspekhi Matematicheskykh Nauk 35:4 (1980), 153-154.

  19. "Hodge Properties of Gauss-Manin Connections," Funktsional'nyi Analiz i ego Prilozheniya 14:1 (1980), 46-47; Functional Analysis and its Applications (Eng. Transl. of FAP) 14 (1980), 34-35.

  20. "The Aymptotics of Holomorphic Forms Determine a Mixed Hodge Structure," Dokl. Acad. Nauk USSR 255 (1980), 1035-1038; Soviet Mathematics Doklady (Eng. Transl. of DAN) 22:5 (1980), 772-775.

  21. "Gauss-Manin Connection of Isolated Singular Point and Bernstein Polynomial," Bull. des Sciences Math. 2e Serie 104 (1980), 205-223.

  22. "The Asymptotics of the Integrals of the Saddle Point Method," Uspekhi Matematicheskykh Nauk 36:4 (1981), 212-213.

  23. "On Obstructions to the Local Equivalence of Distributions," Mat. Zametki 29:6 (1981), 939-947; Math Notes 29:6 (1981), 121-128.

  24. "An Asymptotic Mixed Hodge Structure in Vanishing Cohomologies," Izv. Acad. Sci. USSR, Ser. Mat. 45 (1981), 540-591.

  25. "The Monodromy Operator in Vanishing Cohomologies and the Operator of Multiplication by f in the Local Ring," Doklady Akademii Nauk USSR 260 (1981), 272-276.

  26. "The Complex Index of a Singularity does not Change Along the Strata const, Funktsional'nyi Analiz i ego Prilozheniya 16:1 (1981), 1-12; Functional Analysis and its Applications (Eng. Transl. of FAP) 16 (1981), 1-9.

  27. "On the Number of Integer Points in a Region," Uspekhi Matematicheskykh Nauk 37:3 (1982), 177-178; Russian Mathematics Surveys (Eng. Transl. of Uspekhi Matematicheskykh Nauk) 37:3 (1982), 223-224.

  28. (with A.B. Givental) "Period Maps and Intersection Form,"Funktsional'nyi Analiz i ego Prilozheniya 16:1 (1982), 1-14; Functional Analysis and its Applications (Eng. Transl. of FAP) 16 (1982), 83-93.

  29. "An Estimate from Below of the Codimension of the Stratum const by Mixed Hodge Structures," Vestnik MGU, Ser. Math. 6 (1982), 28-31.

  30. "The Spectrum and Decomposition of Critical Point of Function," Doklady Akademii Nauk USSR 270:2 (1983), 267-270.

  31. "Number of Lattice Points in Families of Homothetic Domains in n, Funktsional'nyi Analiz i ego Prilozheniya 17:2 (1983), 1-6; Functional Analysis and its Applications (Eng. Transl. of FAP) 17 (1983), 79-83.

  32. "On the Semicontinuity of the Spectra and Estimates from above of the Number of Singular Points of a Projective Hypersurfasca," Doklady Akademii Nauk USSR 270:6 (1983), 1294-1297.

  33. "On the Semicontinuity of the Complex Singular Index," Funktsional'nyi Analiz i ego Prilozheniya 17:3 91983), 77-78; Functional Analysis and its Applications (Eng. Transl. of FAP) 17 (19830, 307-309.

  34. "On the Change in Discrete Characteristics of Points of Function Under Deformations," Uspekhi Matematicheskykh Nauk 38:5 (1983), 126-127.

  35. (with A. G. Kouchnirenko) "Singularities of Differential Maps," in "Mathematical Encyclopedia," Vol. 4, 1984, Moscow, pp. 125-131.

  36. (with V.I. Arnol'd, A.B. Givental, A.G. Hovansky) "Singularities of Functions, Wave Fronts, Caustics and Multidimensional Integrals," Mathematical Physics Reviews 4 (1984), 1-92.

  37. (with V.I. Arnol'd, S.M. Gusein-Zade) "Singularities of Differential Maps, Vol. I," Nauka, Moscow, 1982; also Birkhauser, 1985.

  38. "Weight Fibration of Discriminant," Uspekhi Matematicheskykh Nauk 40:5 (1985), 211.

  39. "Asymptotics of Integrals and Hodge Structures," in "Science Reviews: Current Problems in Mathematics, Vol. 22," 1983, pp. 130-166; J. Sov. Math. (1984), Vol. 27.

  40. "Estimate of the Number of Zeros of Real Abelian Integral Depending on a Parameter and Limiting Cycles," Funktsional'nyi Analiz i ego Prilozheniya 18:2 (1984), 1-13; Functional Analysis and its Applications (Eng. Transl. of FAP) 18 (1984), 98-108.

  41. "On Local Residue and Intersection Form in Vanishing Cohomologies," Izvestiya Akademii Nauk USSR, Seriya Mathematicheskaya 48:5 (1984), 1010-1035.

  42. (with S.V. Chmutov) "Finite Irreducible Groups, Generated by Reflections may be Monodromy Groups of Suitable Singularities," Funktsional'nyi Analiz i ego Prilozheniya 18:3 (1984), 1-14; Functional Analysis and its Applications (Eng. Transl. of FAP) 18 (1984), 171-183.

  43. (S.M. Gusein-Zade) "The Topology of Caustics, Wave Fronts and Degenerations of Critical Points," Uspekhi Matematicheskykh Nauk 39:2 (1984), 190-191; Russian Mathematics Surveys (Eng. Transl. of UMN) 39:2, (1984), 209-210.

  44. (with A.G. Hovansky) "Asymptotics of Integrals Over Vanishing Cycles and the Newton Polyhedron, Doklady Akademii Nauk USSR," 283:3 (1985), 521-525; Soviet Mathematics Doklady (Eng. Transl. of DAN) 32 (1985), 122-127.

  45. (S.V. Chmutov) "On the Tangent Cone to the Stratum const," Vestnik MGU, Ser. Math. 1 (1985), 6-9.

  46. "Local Classification of Volume Forms in the Presence of a Hypersurface," Funktsional'nyi Analiz i ego Prilozheniya 19:4 (1985), 23-31; Functional Analysis and its Applications (Eng. Transl. of FAP) 19 (1985), 269-276.

  47. "Geometry of Phase Transitions, Mechanics of Multicomponent Systems (Moscow Institute of Gas and Oil) 200, (1986) 1498-155?

  48. "Combinatorics and Topology of Configuration of Affine Hyperplanes in Real Space,"Funktsional'nyi Analiz i ego Prilozheniya 21:1 (1987), 11-22.

  49. (with I.M. Gelfand) "On Heaviside Functions of Configuration of Hyperplane," Funktsional'nyi Analiz i ego Prilozheniya 21:4 (1987), 1-18.

  50. "On Normal Forms of Non-Smoothness of Solutions of Hyperbolic Equations," Izvestiya Akademii Nauk USSR, Seriya Matematicheskaya 51:4 (1987), 652-665.

  51. "The Image of the Period Map for Simple Singularities," in "Methods of Contemporary Functional Analysis in Geometry and Topology," Voronezh State University 1987, pp. 47-60.

  52. "The Period Mapping and the Discriminant," Mat. Sbornik 134:1 (1987), 66-81.

  53. (with V.I. Arnol'd, S.M. Gusein-Zade) "Singularities of Differential Maps, Vol. II," Nauka, Moscow, 1984; Birkhauser, 1988.

  54. (with D. Barlet) "Around the Intersection Form of an Isolated Singularity of Hypersurface,"Compositio Math. 67 (1988), 149-163; Uspekhi Matematicheskykh Nauk 43:3 (1988), 240-241.

  55. "On the Number of Facets of Configuration of Hyperplanes," Doklady Akademii Nauk USSR 302:3 (1988), 527-530.

  56. "Bifurcations of Convex Hulls and Phase Transitions in Thermodynamics," Science Reviews: Current Problems in Mathematics 33 (1988), 157-191.

  57. "Functional Equations in Volume Mapping," Mat. Zametky 44:4 (1988), 417-427.

  58. (with A.V. Kazarnovski) "Phase Transitions of Multicomponent Systems," in "Filtration in Porous Medium," Moscow Institute of Gas and Oil, 1988, pp. 86-101.

  59. "Multidimensional Vandermonde Determinant," Uspekhi Matematicheskykh Nauk 43:4 (1988), p. 190.

  60. with A.A. Beilinson, A.B. Goncharov, V.V. Schechtman) "Aomoto Dilogarithms, Mixed Hodge Structures and Motivic Cohomology of Pairs of Triangles on the Plane," in "The Grothendieck Festschrift," Vol. I, Birkhauser, pp. 135-172, 1990.

  61. (with V.V. Schechtman) "Integral Representations of N-Point Conformal Correlators in the WZW Model," Bonn, Max-Planck Institute, 1989, pp. 1-22.

  62. "Beta-Function of Euler, Vandermonde Determinant, Legendre Equation and Critical Values of Linear Functions of Configuration of Hyperplanes," I. Izvestiya Akademii Nauk USSR, Seriya Matematicheskaya, 53:6 (1989), 1206-1235.

  63. "Determinant of Matrix of Multidimensional Hypergeometric Integrals," Doklady Akademii Nauk USSR 308, N4 (1989), 777-780.

  64. "Critical Values and Determinant of Periods," Upsekhi Matematicheskvkh Nauk 44:4 (1989), 235-236.

  65. "Hodge Filtration of Hypergeometric Integrals Associated with an Affine Configuration of General Position and a Local Torelli Theorem," Preprint, Michigan University (1990), 1-13.

  66. (with A. Belinson, A. Goncharov, V. Schechtman) "Projective Geometry and K-theory," Algebra and Analysis 3 (1990), 78-130.

  67. "Period Mapping, in "Proceedings of the School on Operator Theory," Kuybishev, 1989, pp. 5-15.

  68. "Beta-Function of Euler, Vandermonde Determinant, Legendre Equation and Critical Values of Linear Function on Configuration of Hyperplanes, II," Izvestiya Akademii Nauk USSR, Seriya Matematicheskaya 54:1 (1990), 146-158.

  69. (with V.V. Schechtman) "Hypergeometric Solutions of Kniznik-Zamolodchikov Equations," Letters in Math. Physics 20 (1990), 279-283.

  70. (with B.A. Feigin, V.V. Schechtman) "On Algebraic Equations Satisfied by Correlators in WZW Models," Letters in Math. Physics 20 (1990), 291-297.

  71. (with V. Schechtman) "Arrangements of Hyperplanes and Lie Algebra Homology," Invent. Math. Vol. 106 (1991), 139-194.

  72. (with V. Schechtman) "Quantum Groups and Homology of Local Systems," ICM-90 Satellite Conf. Proc., Algebraic Geometry and Analytic Geometry, Springer Verlag, (1991), 182-197.

  73. "Determinant Formula for Selberg Integrals," Funct. Analysis and its Applications, 25 (1991), no. 4, 88-89.

  74. "Multidimensional Hypergeometric Functions in Conformal Field theory," Algebraic K-Theory, Algebraic Geometry, Proc. ICM-90, Vol. I, (1991) 281-300.

  75. (with P. Etingof) "Why the Boundary of a Round Drop Becomes a Curve of Order Four," University Lecture Series, V. 3, AMS, 1992.

  76. (with B. Blok) "Topological Conformal Field Theories and Flat Coordinates," Intern. Journal of Modern Physics A, Vol. 7 (1992) 1467-1490.

  77. (with A. Zazovski) "Three-Phase Filtration of Non-Mixed Fluids," in Special Sections of Mechanics, Science Reviews, V. 4 (1992) 98-153 (in Russian).

  78. "Period Maps Connected with a Versal Deformation of a Critical Point of a Function, and the Discriminant," Amer. Math. Soc. Transl. (2) Vol. 153, (1992), pp 1-9.

  79. "Hypergeometric Functions and the Representation Theory of Lie Algebras and Quantum Groups," Advanced Series in Mathematical Physics, Vol. 21, World Scientific (1995).

  80. "A Geometric Approach to Representation Theory of Quantum Groups," 20th Int. Conf. on Diff. Geo. Methods in Theor. Phys. World Scientific, 1992, Vol. 1, 152-175.

  81. "Hodge Filtration of Hypergeometric Integrals Associated with an Affine Configuraiton of General Position and Local Torelli Theorem," Advances in Soviet Mathematics, 16 (1993) 167-177.

  82. (with T. Brylawski) "Determinant Formula for a Matroid BIlinear Form," Advances in Math., Vol. 129, No. 1, 1-24.

  83. "Bilinear Form of Real Configuration of Hyperplane," Adv. in Math., 97 (1993), 110-144.

  84. "Quantized Knizhnik-Zamolodchikov Equations," Quantum Yang-Baxter Equation, and Difference Equations for q-Hypergeometric Functions, Comm. Math. Phys., 162, 499-528 (1994).

  85. (with V. Schechtman & B. Feigin) "On Algebraic Equations Satisfied by Hypergeometric Correlators in WZW Models I," Comm. Math. Phys., 163, 173-184 (1994).

  86. (with V. Tarasov) "Jackson Integral Representations for Solutions of the Quantized Knizhnik-Zamolodchikov Equations," St. Petersburg Math. Journal, 6, no. 2, 275-313 (1994).

  87. General Hypergeometric Functions & Representation Theory of Lie Groups & Lie Algebras, Advanced Series in Mathematical Physics, Vol. 21, 1995.

  88. (with B. Feigin, V. Schechtman) "On Algebraic Equations Satisfied by Hypergeometric Correlators in WZW Models, II," Comm. in Math. Phys. v. 170, (1995) No. 1, 219-247.

  89. (with N. Reshetikhin) "Quasiclassical Asymptotics of Solutions to the KZ Equations," Geometry, Topology and Physics for R. Bott, intern. Press (1995) 293-322.

  90. "Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors," preprint (1993), Compos. Math., 97, 385-401.

  91. "Asymptotic Solutions to the KZ Equation and Crystal Base," Comm. in Math. Phys. 171 (1995) 99-137.

  92. (with V. Schechtman, H. Terao) "Local Systems Over Complements of Hyperplanes and the Kac-Kazhdan Conditions for Singular Vectors," Journal of Pure and Applied Algebra, 100th issue (1995) 93-102.

  93. (with G. Felder) "Integral Representation of Solutions of the Elliptic Knizhnik-Zamolodchikov-Bernard Equations," preprint, Int. Math. Res. Notices, (1995) No. 5, 221-223.

  94. (with G. Felder) "Three Formulas for Eigenfunctions of Integrable Schrodinger Operators," Compsitio Math. 107 (1997), 143-175.

  95. (with G. Felder) "On Representations of the Elliptic Quantum Group Comm. Math. Phys. 181, (1996), 741-761.

  96. (with V. Tarasov) "Completeness of Bethe Vectors and Difference Equations with Regular Singular Points," Int. Math. Res. Notices, (1995) No. 13, 637-669.

  97. (with V. Tarsov) "Solutions to the Quantized KZ Equation & the Bethe Ansatz," Proceeding of the XX-th ICGTMP, Group Theoretical Methods in Physics (Arima, Eguchi, Nakanishi eds) World Scientific, (1995) 473-478.

  98. (with V. Tarasov) "Completeness of Bethe Vectors and Difference Equations with Regular Singular Points," Int. Math. Res. Notices, (1995) No. 13, 637-669.

  99. (with V. Schechtman & H. Terao) "Local Systems over Complements of Hyperplanes & the Kac-Kazhdan Conditions for Singular Vectors," Journal of Pure & Applied Algebra, 100th issue (1995) 93-102.

  100. (with G. Felder) "Remarks on the Structure Constants of the Verlinde Algebra Associated to s13," Letters in Math. Physics, Vol. 37 (1996) 167-172.

  101. (with G. Felder) "On Representations of the Elliptic Quantum Group Comm. Math. Phys. 181, 741-761.

  102. (with V. Tarasov) "Asymptotic Solutions to the Quantized KZ Equation & Bethe Vectors," American Math. Society Transl. (2) Vol. 174, (1996) 235-273.

  103. (with S. Chmutov) "Remarks on the Vassiliev Knot Invariants Coming from s12," Topology, Vol. 36, No. 1, (1996) 153-178.

  104. (with G. Felder) "Algebraic Bethe Ansatz for the Elliptic Quantum Group Nuclear Physics B 480 (1996) 485-503.

  105. (with V. Tarasov) "Geometry of q-hypergeometric Functions as a Bridge Between Yangians and Quantum Affine Algebras," Invent. Math. 128 (1997) 501-588.

  106. (with S. Gussein-Zade) "Verlinde Algebras and the Intersection Form on Vanishing Cycles," Selecta Mathematica, New Series, 3(1997) 79-97.

  107. (with G. Felder, V. Tarasov) "Solutions of the Elliptic QKZB Equations and Bethe Ansatz I," in Topics in Singularity Theory, V.I. Arnold's 60th Anniversary Collection, Advances in the Mathematical Sciences 34, AMS Translations, Series 2, V. 180 (1997) 45-76.

  108. (with I. Frenkel, A. Kirillov) "Canonical Basis and Homology of Local Systems," Int. Math. Res. Notices, No. 16, (1997) 783-806.

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