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Publications in Math-Net.Ru |
Citations |
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2023 |
1. |
Pavel Etingof, Alexander Varchenko, “Polynomial Solutions Modulo $p^s$ of Differential KZ and Dynamical Equations”, SIGMA, 19 (2023), 061, 16 pp. |
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2022 |
2. |
Giordano Cotti, Alexander Varchenko, “The $*$-Markov equation for Laurent polynomials”, Mosc. Math. J., 22:1 (2022), 1–68 |
2
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3. |
A. Varchenko, “Dynamical and qKZ Equations Modulo
$p^s$:
an Example”, Math. Notes, 112:6 (2022), 1003–1016 |
1
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2021 |
4. |
A. N. Varchenko, “An Invariant Subbundle of the KZ Connection mod
$p$
and Reducibility of
$\widehat{\mathfrak{sl}_2}$
Verma Modules mod $p$”, Math. Notes, 109:3 (2021), 386–397 |
5
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2019 |
5. |
Andrew Prudhom, Alexander Varchenko, “Potentials of a family of arrangements of hyperplanes and elementary subarrangements”, Mosc. Math. J., 19:1 (2019), 153–180 |
1
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6. |
Richárd Rimányi, Andrey Smirnov, Alexander Varchenko, Zijun Zhou, “Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety”, SIGMA, 15 (2019), 093, 22 pp. |
19
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7. |
Alexey Slinkin, Alexander Varchenko, “Twisted de Rham Complex on Line and Singular Vectors in $\widehat{{\mathfrak{sl}_2}}$ Verma Modules”, SIGMA, 15 (2019), 075, 26 pp. |
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2018 |
8. |
Giovanni Felder, Richárd Rimányi, Alexander Varchenko, “Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology”, SIGMA, 14 (2018), 132, 41 pp. |
12
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2017 |
9. |
Vadim Schechtman, Alexander Varchenko, “Rational differential forms on the line and singular vectors in Verma modules over $\widehat{sl}_2$”, Mosc. Math. J., 17:4 (2017), 787–802 |
3
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2015 |
10. |
Alexander Varchenko, Charles A. S. Young, “Populations of Solutions to Cyclotomic Bethe Equations”, SIGMA, 11 (2015), 091, 41 pp. |
1
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2013 |
11. |
Vitaly Tarasov, Alexander Varchenko, “Combinatorial Formulae for Nested Bethe Vectors”, SIGMA, 9 (2013), 048, 28 pp. |
26
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2012 |
12. |
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “KZ characteristic variety as the zero set of classical Calogero–Moser Hamiltonians”, SIGMA, 8 (2012), 072, 11 pp. |
22
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2011 |
13. |
A. N. Varchenko, R. Rimányi, V. O. Tarasov, V. V. Schechtman, “Cohomology of a flag variety as a Bethe algebra”, Funktsional. Anal. i Prilozhen., 45:4 (2011), 16–31 ; Funct. Anal. Appl., 45:4 (2011), 252–264 |
6
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14. |
Richárd Rimányi, Vadim Schechtman, Alexander Varchenko, “Conformal blocks and equivariant cohomology”, Mosc. Math. J., 11:3 (2011), 561–581 |
2
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15. |
Alexander Varchenko, “Quantum Integrable Model of an Arrangement of Hyperplanes”, SIGMA, 7 (2011), 032, 55 pp. |
19
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2010 |
16. |
E. Mukhin, V. Tarasov, A. Varchenko, “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 ; St. Petersburg Math. J., 22:3 (2011), 463–472 |
24
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17. |
A. Varchenko, “A Selberg integral type formula for an $\mathfrak{sl}_2$ one-dimensional space of conformal blocks”, Mosc. Math. J., 10:2 (2010), 469–475 |
5
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2007 |
18. |
E. E. Mukhin, V. O. Tarasov, A. N. Varchenko, “Higher Lamé equations and critical points of master functions”, Mosc. Math. J., 7:3 (2007), 533–542 |
3
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19. |
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel”, SIGMA, 3 (2007), 060, 31 pp. |
17
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20. |
E. E. Mukhin, V. Schechtman, V. O. Tarasov, A. N. Varchenko, “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 ; Proc. Steklov Inst. Math., 258 (2007), 155–177 |
2
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2006 |
21. |
A. N. Varchenko, “Bethe ansatz for arrangements of hyperplanes and the Gaudin model”, Mosc. Math. J., 6:1 (2006), 195–210 |
17
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2003 |
22. |
I. G. Scherbak, A. N. Varchenko, “Critical points of functions, $\mathfrak{sl}_2$ representations, and Fuchsian differential equations with only univalued solutions”, Mosc. Math. J., 3:2 (2003), 621–645 |
37
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23. |
G. Felder, L. J. Stevens, A. N. Varchenko, “Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator”, Mosc. Math. J., 3:2 (2003), 457–473 |
2
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24. |
A. N. Varchenko, S. Tyurina, “A remark on the $sl_2$ approximation of the Kontsevich integral of the unknot”, Zap. Nauchn. Sem. POMI, 299 (2003), 30–37 ; J. Math. Sci. (N. Y.), 131:1 (2005), 5270–5274 |
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2001 |
25. |
V. O. Tarasov, A. N. Varchenko, “Small elliptic quantum group $e_{\tau,\gamma}(\mathfrak{sl}_N)$”, Mosc. Math. J., 1:2 (2001), 243–286 |
9
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1998 |
26. |
A. N. Varchenko, G. Felder, “Algebraic Integrability of the Two-Body Ruijsenaars Operator”, Funktsional. Anal. i Prilozhen., 32:2 (1998), 8–25 ; Funct. Anal. Appl., 32:2 (1998), 81–92 |
9
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1994 |
27. |
A. N. Varchenko, V. O. Tarasov, “Jackson integral representations for solutions of the Knizhnik–Zamolodchikov quantum equation”, Algebra i Analiz, 6:2 (1994), 90–137 ; St. Petersburg Math. J., 6:2 (1995), 275–313 |
39
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1992 |
28. |
A. N. Varchenko, “Combinatorics of a partial fraction decomposition”, Trudy Mat. Inst. Steklov., 193 (1992), 49–52 ; Proc. Steklov Inst. Math., 193 (1993), 51–55 |
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1991 |
29. |
A. N. Varchenko, “Determinant formula for Selberg-type integrals”, Funktsional. Anal. i Prilozhen., 25:4 (1991), 88–89 ; Funct. Anal. Appl., 25:4 (1991), 304–305 |
3
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1990 |
30. |
A. A. Beilinson, A. N. Varchenko, A. B. Goncharov, V. V. Schechtman, “Projective geometry and $K$-theory”, Algebra i Analiz, 2:3 (1990), 78–130 ; Leningrad Math. J., 2:3 (1991), 523–576 |
1
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31. |
A. N. Varchenko, “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 ; Math. USSR-Izv., 36:1 (1991), 155–167 |
9
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1989 |
32. |
A. N. Varchenko, “The determinant of a matrix of multidimensional hypergeometric
integrals”, Dokl. Akad. Nauk SSSR, 308:4 (1989), 777–780 ; Dokl. Math., 40:2 (1990), 359–362 |
1
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33. |
A. N. Varchenko, “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 ; Math. USSR-Izv., 35:3 (1990), 543–571 |
21
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34. |
A. N. Varchenko, “Critical values and the determinant of the periods”, Uspekhi Mat. Nauk, 44:4(268) (1989), 235–236 ; Russian Math. Surveys, 44:4 (1989), 209–210 |
5
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1988 |
35. |
A. N. Varchenko, “The numbers of faces of a configuration of hyperplanes”, Dokl. Akad. Nauk SSSR, 302:3 (1988), 527–530 ; Dokl. Math., 38:2 (1989), 291–295 |
36. |
A. N. Varchenko, “Rearrangements of convex hulls and phase transitions in thermodynamics”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 33 (1988), 157–191 ; J. Soviet Math., 52:4 (1990), 3305–3325 |
12
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37. |
A. N. Varchenko, “Functional equations for a volume map”, Mat. Zametki, 44:4 (1988), 417–427 ; Math. Notes, 44:4 (1988), 707–712 |
2
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1987 |
38. |
A. N. Varchenko, I. M. Gel'fand, “Heaviside functions of a configuration of hyperplanes”, Funktsional. Anal. i Prilozhen., 21:4 (1987), 1–18 ; Funct. Anal. Appl., 21:4 (1987), 255–270 |
15
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39. |
A. N. Varchenko, “Combinatorics and topology of the disposition of affine hyperplanes in real space”, Funktsional. Anal. i Prilozhen., 21:1 (1987), 11–22 ; Funct. Anal. Appl., 21:1 (1988), 9–19 |
22
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40. |
A. N. Varchenko, “On normal forms of nonsmoothness of solutions of hyperbolic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987), 652–665 ; Math. USSR-Izv., 30:3 (1988), 615–628 |
3
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41. |
A. N. Varchenko, “The period map and the discriminant”, Mat. Sb. (N.S.), 134(176):1(9) (1987), 66–81 ; Math. USSR-Sb., 62:1 (1989), 65–81 |
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1985 |
42. |
A. N. Varchenko, A. G. Khovanskii, “Asymptotic behavior of integrals over vanishing cycles and the Newton polyhedron”, Dokl. Akad. Nauk SSSR, 283:3 (1985), 521–525 |
1
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43. |
A. N. Varchenko, “Local classification of volume forms in the presence of a hypersurface”, Funktsional. Anal. i Prilozhen., 19:4 (1985), 23–31 ; Funct. Anal. Appl., 19:4 (1985), 269–276 |
6
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44. |
A. N. Varchenko, “On the local residue and the intersection form on the vanishing cohomology”, Izv. Akad. Nauk SSSR Ser. Mat., 49:1 (1985), 32–54 ; Math. USSR-Izv., 26:1 (1986), 31–52 |
16
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45. |
A. N. Varchenko, S. V. Chmutov, “On the tangent cone to the stratum $\mu=\operatorname{const}$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 1, 6–9 |
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1984 |
46. |
A. N. Varchenko, S. V. Chmutov, “Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities”, Funktsional. Anal. i Prilozhen., 18:3 (1984), 1–13 ; Funct. Anal. Appl., 18:3 (1984), 171–183 |
7
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47. |
A. N. Varchenko, “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 ; Funct. Anal. Appl., 18:2 (1984), 98–108 |
83
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48. |
A. N. Varchenko, S. M. Gusein-Zade, “The topology of caustics, wave fronts, and degeneracies of critical points”, Uspekhi Mat. Nauk, 39:2(236) (1984), 141–142 ; Russian Math. Surveys, 39:2 (1984), 209–210 |
3
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1983 |
49. |
A. N. Varchenko, “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 |
6
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50. |
A. N. Varchenko, “The spectrum and decompositions of a critical point of a function”, Dokl. Akad. Nauk SSSR, 270:2 (1983), 267–270 |
1
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51. |
A. N. Varchenko, “Semicontinuity of the complex singularity index”, Funktsional. Anal. i Prilozhen., 17:4 (1983), 77–78 ; Funct. Anal. Appl., 17:4 (1983), 307–309 |
5
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52. |
A. N. Varchenko, “Number of lattice points in families of homothetic domains in $\mathbb{R}^n$”, Funktsional. Anal. i Prilozhen., 17:2 (1983), 1–6 ; Funct. Anal. Appl., 17:2 (1983), 79–83 |
19
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53. |
A. N. Varchenko, “Asymptotic behaviors of integrals, and Hodge structures”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 22 (1983), 130–166 ; J. Soviet Math., 27:3 (1984), 2760–2784 |
6
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1982 |
54. |
A. N. Varchenko, A. B. Givental', “Mapping of periods and intersection form”, Funktsional. Anal. i Prilozhen., 16:2 (1982), 7–20 ; Funct. Anal. Appl., 16:2 (1982), 83–93 |
19
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55. |
A. N. Varchenko, “The complex exponent of a singularity does not change along strata $\mu=\mathrm{const}$”, Funktsional. Anal. i Prilozhen., 16:1 (1982), 1–12 ; Funct. Anal. Appl., 16:1 (1982), 1–9 |
106
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56. |
A. N. Varchenko, “On the number of integral points in a domain”, Uspekhi Mat. Nauk, 37:3(225) (1982), 177–178 ; Russian Math. Surveys, 37:3 (1982), 223–224 |
4
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57. |
A. N. Varchenko, “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 |
2
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1981 |
58. |
A. N. Varchenko, “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 |
1
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59. |
A. N. Varchenko, “Asymptotic Hodge structure in the vanishing cohomology”, Izv. Akad. Nauk SSSR Ser. Mat., 45:3 (1981), 540–591 ; Math. USSR-Izv., 18:3 (1982), 469–512 |
54
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60. |
A. N. Varchenko, “Obstructions to local equivalence of distributions”, Mat. Zametki, 29:6 (1981), 939–947 ; Math. Notes, 29:6 (1981), 479–484 |
4
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1980 |
61. |
A. N. Varchenko, “The asymptotics of holomorphic forms determine a mixed Hodge structure”, Dokl. Akad. Nauk SSSR, 255:5 (1980), 1035–1038 |
5
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62. |
A. N. Varchenko, “Hodge properties of Gauss–Manin connectivities”, Funktsional. Anal. i Prilozhen., 14:1 (1980), 46–47 ; Funct. Anal. Appl., 14:1 (1980), 36–37 |
6
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1979 |
63. |
A. N. Varchenko, “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 ; Funct. Anal. Appl., 13:1 (1979), 52–53 |
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1978 |
64. |
A. N. Varchenko, “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 ; Russian Math. Surveys, 33:6 (1978), 263–264 |
1
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1977 |
65. |
A. N. Varchenko, S. A. Molchanov, “Applications of the method of stationary phase in limit theorems for Markov chains”, Dokl. Akad. Nauk SSSR, 233:1 (1977), 11–14 |
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1976 |
66. |
A. N. Varchenko, “Newton polyhedra and estimation of oscillating integrals”, Funktsional. Anal. i Prilozhen., 10:3 (1976), 13–38 ; Funct. Anal. Appl., 10:3 (1976), 175–196 |
108
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1975 |
67. |
A. N. Varchenko, “A theorem on topological versal deformation”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975), 294–314 ; Math. USSR-Izv., 9:2 (1975), 277–296 |
1
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1974 |
68. |
A. N. Varchenko, “Local topological properties of differentiable mappings”, Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974), 1037–1090 ; Math. USSR-Izv., 8:5 (1974), 1033–1082 |
6
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1973 |
69. |
A. N. Varchenko, “The relation between topological and algebro-geometric equisingularities according to Zariski”, Funktsional. Anal. i Prilozhen., 7:2 (1973), 1–5 ; Funct. Anal. Appl., 7:2 (1973), 87–90 |
5
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70. |
A. N. Varchenko, “Local topological properties of analytic mappings”, Izv. Akad. Nauk SSSR Ser. Mat., 37:4 (1973), 883–916 ; Math. USSR-Izv., 7:4 (1973), 883–917 |
6
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71. |
A. N. Varchenko, “The germs of differentiable mappings whose topological type is determined by a finite jet”, Uspekhi Mat. Nauk, 28:3(171) (1973), 175–176 |
1
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1972 |
72. |
A. N. Varchenko, “On the germs of analytic mappings whose topological type is determined by a finite jet”, Funktsional. Anal. i Prilozhen., 6:3 (1972), 63–64 ; Funct. Anal. Appl., 6:3 (1972), 225–227 |
3
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73. |
A. N. Varchenko, “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 ; Math. USSR-Izv., 6:5 (1972), 949–1008 |
28
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1971 |
74. |
A. N. Varchenko, “A theorem on the equisingularity of families of algebraic varieties”, Uspekhi Mat. Nauk, 26:1(157) (1971), 217–218 |
3
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1969 |
75. |
A. N. Varchenko, “On the bifurcation of multiple integrals depending on a parameter”, Funktsional. Anal. i Prilozhen., 3:4 (1969), 79–80 ; Funct. Anal. Appl., 3:4 (1969), 322–324 |
5
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2021 |
76. |
V. M. Buchstaber, A. N. Varchenko, A. P. Veselov, P. G. Grinevich, S. Grushevsky, S. Yu. Dobrokhotov, A. V. Zabrodin, A. V. Marshakov, A. E. Mironov, N. A. Nekrasov, S. P. Novikov, A. Yu. Okounkov, M. A. Olshanetsky, A. K. Pogrebkov, I. A. Taimanov, M. A. Tsfasman, L. O. Chekhov, O. K. Sheinman, S. B. Shlosman, “Igor' Moiseevich Krichever (on his 70th birthday)”, Uspekhi Mat. Nauk, 76:4(460) (2021), 183–193 ; Russian Math. Surveys, 76:4 (2021), 733–743 |
1
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77. |
A. N. Varchenko, A. M. Slinkin, D. Thompson, “Dynamical $\mathfrak{sl}_2$ Bethe algebra and functions on pairs of quasi-polynomials”, Uspekhi Mat. Nauk, 76:4(460) (2021), 105–138 ; Russian Math. Surveys, 76:4 (2021), 653–684 |
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2011 |
78. |
A. N. Varchenko, S. M. Gusein-Zade, “V. I. Arnold: 12.06.1937 – 03.06.2010”, Tr. Mosk. Mat. Obs., 72:1 (2011), 1–4 ; Trans. Moscow Math. Soc., 72 (2011), viii–xi |
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2010 |
79. |
S. B. Artemov, A. A. Belavin, V. M. Buchstaber, A. I. Esterov, B. L. Feigin, V. A. Ginzburg, E. A. Gorsky, Yu. S. Ilyashenko, A. A. Kirillov, A. G. Khovanskii, S. K. Lando, G. A. Margulis, Yu. A. Neretin, S. P. Novikov, S. B. Shlosman, A. B. Sossinsky, M. A. Tsfasman, A. N. Varchenko, V. A. Vassiliev, S. G. Vlăduţ, “Sabir Medgidovich Gusein-Zade”, Mosc. Math. J., 10:4 (2010), 831–832 |
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2009 |
80. |
A. M. Abramov, V. I. Arnol'd, A. V. Bolsinov, A. N. Varchenko, L. Galgani, B. I. Zhilinskii, Yu. S. Il'yashenko, V. V. Kozlov, A. I. Neishtadt, V. I. Piterbarg, A. G. Khovanskii, V. V. Yashchenko, “Nikolai Nikolaevich Nekhoroshev (obituary)”, Uspekhi Mat. Nauk, 64:3(387) (2009), 174–178 ; Russian Math. Surveys, 64:3 (2009), 561–566 |
3
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2007 |
81. |
A. N. Varchenko, V. A. Vassiliev, S. M. Gusein-Zade, A. A. Davydov, V. M. Zakalyukin, Yu. S. Ilyashenko, M. E. Kazarian, A. G. Kushnirenko, S. K. Lando, A. G. Khovanskii, “Vladimir Igorevich Arnold in the Eyes of His Students: On the occasion of his 70th birthday”, Trudy Mat. Inst. Steklova, 259 (2007), 5–9 ; Proc. Steklov Inst. Math., 259 (2007), 1–5 |
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1988 |
82. |
V. M. Kharlamov, A. N. Varchenko, V. M. Petkov, Ya. G. Sinai, K. M. Khanin, S. Yu. Dobrokhotov, A. B. Givental', V. A. Dobrynin, “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 |
3
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1982 |
83. |
L. V. Keldysh, N. V. Nikolenko, A. N. Varchenko, A. S. Kalashnikov, V. L. Berdichevsky, D. G. Vasil'ev, V. B. Lidskii, A. I. Vol'pert, V. M. Kamenkovich, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 37:5(227) (1982), 221–226 |
6
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1978 |
84. |
V. I. Arnol'd, A. L. Gol'denveizer, V. B. Lidskii, I. M. Krichever, A. N. Varchenko, R. L. Dobrushin, A. A. Barmin, S. V. Manakov, V. A. Malyshev, R. A. Minlos, L. D. Faddeev, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 33:2(200) (1978), 225–231 |
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