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Varchenko Aleksandr Nikolaevich

Publications in Math-Net.Ru

  1. Polynomial Solutions Modulo $p^s$ of Differential KZ and Dynamical Equations

    SIGMA, 19 (2023), 061, 16 pp.
  2. The $*$-Markov equation for Laurent polynomials

    Mosc. Math. J., 22:1 (2022),  1–68
  3. Dynamical and qKZ Equations Modulo $p^s$: an Example

    Mat. Zametki, 112:6 (2022),  1003–1016
  4. An Invariant Subbundle of the KZ Connection mod $p$ and Reducibility of $\widehat{\mathfrak{sl}_2}$ Verma Modules mod $p$

    Mat. Zametki, 109:3 (2021),  386–397
  5. Potentials of a family of arrangements of hyperplanes and elementary subarrangements

    Mosc. Math. J., 19:1 (2019),  153–180
  6. Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety

    SIGMA, 15 (2019), 093, 22 pp.
  7. Twisted de Rham Complex on Line and Singular Vectors in $\widehat{{\mathfrak{sl}_2}}$ Verma Modules

    SIGMA, 15 (2019), 075, 26 pp.
  8. Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology

    SIGMA, 14 (2018), 132, 41 pp.
  9. Rational differential forms on the line and singular vectors in Verma modules over $\widehat{sl}_2$

    Mosc. Math. J., 17:4 (2017),  787–802
  10. Populations of Solutions to Cyclotomic Bethe Equations

    SIGMA, 11 (2015), 091, 41 pp.
  11. Combinatorial Formulae for Nested Bethe Vectors

    SIGMA, 9 (2013), 048, 28 pp.
  12. KZ characteristic variety as the zero set of classical Calogero–Moser Hamiltonians

    SIGMA, 8 (2012), 072, 11 pp.
  13. Cohomology of a flag variety as a Bethe algebra

    Funktsional. Anal. i Prilozhen., 45:4 (2011),  16–31
  14. Conformal blocks and equivariant cohomology

    Mosc. Math. J., 11:3 (2011),  561–581
  15. Quantum Integrable Model of an Arrangement of Hyperplanes

    SIGMA, 7 (2011), 032, 55 pp.
  16. Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\frak{gl}_N$

    Algebra i Analiz, 22:3 (2010),  177–190
  17. A Selberg integral type formula for an $\mathfrak{sl}_2$ one-dimensional space of conformal blocks

    Mosc. Math. J., 10:2 (2010),  469–475
  18. Higher Lamé equations and critical points of master functions

    Mosc. Math. J., 7:3 (2007),  533–542
  19. Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel

    SIGMA, 3 (2007), 060, 31 pp.
  20. On a New Form of Bethe Ansatz Equations and Separation of Variables in the $\mathfrak{sl}_3$ Gaudin model

    Trudy Mat. Inst. Steklova, 258 (2007),  162–184
  21. Bethe ansatz for arrangements of hyperplanes and the Gaudin model

    Mosc. Math. J., 6:1 (2006),  195–210
  22. Critical points of functions, $\mathfrak{sl}_2$ representations, and Fuchsian differential equations with only univalued solutions

    Mosc. Math. J., 3:2 (2003),  621–645
  23. Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator

    Mosc. Math. J., 3:2 (2003),  457–473
  24. A remark on the $sl_2$ approximation of the Kontsevich integral of the unknot

    Zap. Nauchn. Sem. POMI, 299 (2003),  30–37
  25. Small elliptic quantum group $e_{\tau,\gamma}(\mathfrak{sl}_N)$

    Mosc. Math. J., 1:2 (2001),  243–286
  26. Algebraic Integrability of the Two-Body Ruijsenaars Operator

    Funktsional. Anal. i Prilozhen., 32:2 (1998),  8–25
  27. Jackson integral representations for solutions of the Knizhnik–Zamolodchikov quantum equation

    Algebra i Analiz, 6:2 (1994),  90–137
  28. Combinatorics of a partial fraction decomposition

    Trudy Mat. Inst. Steklov., 193 (1992),  49–52
  29. Determinant formula for Selberg-type integrals

    Funktsional. Anal. i Prilozhen., 25:4 (1991),  88–89
  30. Projective geometry and $K$-theory

    Algebra i Analiz, 2:3 (1990),  78–130
  31. The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. II

    Izv. Akad. Nauk SSSR Ser. Mat., 54:1 (1990),  146–158
  32. The determinant of a matrix of multidimensional hypergeometric integrals

    Dokl. Akad. Nauk SSSR, 308:4 (1989),  777–780
  33. The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I

    Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989),  1206–1235
  34. Critical values and the determinant of the periods

    Uspekhi Mat. Nauk, 44:4(268) (1989),  235–236
  35. The numbers of faces of a configuration of hyperplanes

    Dokl. Akad. Nauk SSSR, 302:3 (1988),  527–530
  36. Rearrangements of convex hulls and phase transitions in thermodynamics

    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 33 (1988),  157–191
  37. Functional equations for a volume map

    Mat. Zametki, 44:4 (1988),  417–427
  38. Heaviside functions of a configuration of hyperplanes

    Funktsional. Anal. i Prilozhen., 21:4 (1987),  1–18
  39. Combinatorics and topology of the disposition of affine hyperplanes in real space

    Funktsional. Anal. i Prilozhen., 21:1 (1987),  11–22
  40. On normal forms of nonsmoothness of solutions of hyperbolic equations

    Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987),  652–665
  41. The period map and the discriminant

    Mat. Sb. (N.S.), 134(176):1(9) (1987),  66–81
  42. Asymptotic behavior of integrals over vanishing cycles and the Newton polyhedron

    Dokl. Akad. Nauk SSSR, 283:3 (1985),  521–525
  43. Local classification of volume forms in the presence of a hypersurface

    Funktsional. Anal. i Prilozhen., 19:4 (1985),  23–31
  44. On the local residue and the intersection form on the vanishing cohomology

    Izv. Akad. Nauk SSSR Ser. Mat., 49:1 (1985),  32–54
  45. On the tangent cone to the stratum $\mu=\operatorname{const}$

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 1,  6–9
  46. Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities

    Funktsional. Anal. i Prilozhen., 18:3 (1984),  1–13
  47. Estimate of the number of zeros of an abelian integral depending on a parameter and limit cycles

    Funktsional. Anal. i Prilozhen., 18:2 (1984),  14–25
  48. The topology of caustics, wave fronts, and degeneracies of critical points

    Uspekhi Mat. Nauk, 39:2(236) (1984),  141–142
  49. Semicontinuity of the spectrum and an upper bound for the number of singular points of the projective hypersurface

    Dokl. Akad. Nauk SSSR, 270:6 (1983),  1294–1297
  50. The spectrum and decompositions of a critical point of a function

    Dokl. Akad. Nauk SSSR, 270:2 (1983),  267–270
  51. Semicontinuity of the complex singularity index

    Funktsional. Anal. i Prilozhen., 17:4 (1983),  77–78
  52. Number of lattice points in families of homothetic domains in $\mathbb{R}^n$

    Funktsional. Anal. i Prilozhen., 17:2 (1983),  1–6
  53. Asymptotic behaviors of integrals, and Hodge structures

    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 22 (1983),  130–166
  54. Mapping of periods and intersection form

    Funktsional. Anal. i Prilozhen., 16:2 (1982),  7–20
  55. The complex exponent of a singularity does not change along strata $\mu=\mathrm{const}$

    Funktsional. Anal. i Prilozhen., 16:1 (1982),  1–12
  56. On the number of integral points in a domain

    Uspekhi Mat. Nauk, 37:3(225) (1982),  177–178
  57. A lower bound for the codimension of the $\mu=\operatorname{const}$ stratum in terms of the mixed Hodge structure

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1982, no. 6,  28–31
  58. On the monodromy operator in vanishing cohomology and the operator of multiplication by $f$ in the local ring

    Dokl. Akad. Nauk SSSR, 260:2 (1981),  272–276
  59. Asymptotic Hodge structure in the vanishing cohomology

    Izv. Akad. Nauk SSSR Ser. Mat., 45:3 (1981),  540–591
  60. Obstructions to local equivalence of distributions

    Mat. Zametki, 29:6 (1981),  939–947
  61. The asymptotics of holomorphic forms determine a mixed Hodge structure

    Dokl. Akad. Nauk SSSR, 255:5 (1980),  1035–1038
  62. Hodge properties of Gauss–Manin connectivities

    Funktsional. Anal. i Prilozhen., 14:1 (1980),  46–47
  63. A formula for the ranks of the homology groups of the boundary of an isolated singularity of a surface in $\mathbb{C}^3$ and the Newton diagram

    Funktsional. Anal. i Prilozhen., 13:1 (1979),  65–66
  64. The integrality of the limit of the curvature integral along the boundary of an isolated singularity of a surface in $C^3$

    Uspekhi Mat. Nauk, 33:6(204) (1978),  199–200
  65. Applications of the method of stationary phase in limit theorems for Markov chains

    Dokl. Akad. Nauk SSSR, 233:1 (1977),  11–14
  66. Newton polyhedra and estimation of oscillating integrals

    Funktsional. Anal. i Prilozhen., 10:3 (1976),  13–38
  67. A theorem on topological versal deformation

    Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975),  294–314
  68. Local topological properties of differentiable mappings

    Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974),  1037–1090
  69. The relation between topological and algebro-geometric equisingularities according to Zariski

    Funktsional. Anal. i Prilozhen., 7:2 (1973),  1–5
  70. Local topological properties of analytic mappings

    Izv. Akad. Nauk SSSR Ser. Mat., 37:4 (1973),  883–916
  71. The germs of differentiable mappings whose topological type is determined by a finite jet

    Uspekhi Mat. Nauk, 28:3(171) (1973),  175–176
  72. On the germs of analytic mappings whose topological type is determined by a finite jet

    Funktsional. Anal. i Prilozhen., 6:3 (1972),  63–64
  73. Theorems on the topological equisingularity of families of algebraic varieties and families of polynomial mappings

    Izv. Akad. Nauk SSSR Ser. Mat., 36:5 (1972),  957–1019
  74. A theorem on the equisingularity of families of algebraic varieties

    Uspekhi Mat. Nauk, 26:1(157) (1971),  217–218
  75. On the bifurcation of multiple integrals depending on a parameter

    Funktsional. Anal. i Prilozhen., 3:4 (1969),  79–80

  76. Igor' Moiseevich Krichever (on his 70th birthday)

    Uspekhi Mat. Nauk, 76:4(460) (2021),  183–193
  77. Dynamical $\mathfrak{sl}_2$ Bethe algebra and functions on pairs of quasi-polynomials

    Uspekhi Mat. Nauk, 76:4(460) (2021),  105–138
  78. V. I. Arnold: 12.06.1937 – 03.06.2010

    Tr. Mosk. Mat. Obs., 72:1 (2011),  1–4
  79. Sabir Medgidovich Gusein-Zade

    Mosc. Math. J., 10:4 (2010),  831–832
  80. Nikolai Nikolaevich Nekhoroshev (obituary)

    Uspekhi Mat. Nauk, 64:3(387) (2009),  174–178
  81. Vladimir Igorevich Arnold in the Eyes of His Students: On the occasion of his 70th birthday

    Trudy Mat. Inst. Steklova, 259 (2007),  5–9
  82. Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics (September, 30 – December, 9, 1987)

    Uspekhi Mat. Nauk, 43:3(261) (1988),  239–245
  83. Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics

    Uspekhi Mat. Nauk, 37:5(227) (1982),  221–226
  84. Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics

    Uspekhi Mat. Nauk, 33:2(200) (1978),  225–231

© Steklov Math. Inst. of RAS, 2024