Varchenko, Aleksandr Nikolaevich

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Total publications: 78
Scientific articles: 71
Presentations: 3

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Publications in Math-Net.Ru
1. Andrew Prudhom, Alexander Varchenko, “Potentials of a family of arrangements of hyperplanes and elementary subarrangements”, Mosc. Math. J., 19:1 (2019),  153–180  mathnet
2. 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.  mathnet  isi  scopus
3. 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.  mathnet  isi  scopus
4. Giovanni Felder, Richárd Rimányi, Alexander Varchenko, “Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology”, SIGMA, 14 (2018), 132, 41 pp.  mathnet  isi  scopus
5. 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  mathnet  isi
6. Alexander Varchenko, Charles A. S. Young, “Populations of Solutions to Cyclotomic Bethe Equations”, SIGMA, 11 (2015), 091, 41 pp.  mathnet  isi  scopus
7. Vitaly Tarasov, Alexander Varchenko, “Combinatorial Formulae for Nested Bethe Vectors”, SIGMA, 9 (2013), 048, 28 pp.  mathnet  mathscinet  isi  scopus
8. Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “KZ characteristic variety as the zero set of classical Calogero–Moser Hamiltonians”, SIGMA, 8 (2012), 072, 11 pp.  mathnet  mathscinet  isi  scopus
9. 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  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 45:4 (2011), 252–264  isi  elib  scopus
10. Richárd Rimányi, Vadim Schechtman, Alexander Varchenko, “Conformal blocks and equivariant cohomology”, Mosc. Math. J., 11:3 (2011),  561–581  mathnet  mathscinet  isi
11. Alexander Varchenko, “Quantum Integrable Model of an Arrangement of Hyperplanes”, SIGMA, 7 (2011), 032, 55 pp.  mathnet  mathscinet  isi  scopus
12. 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  mathnet  mathscinet  zmath; St. Petersburg Math. J., 22:3 (2011), 463–472  isi  scopus
13. 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  mathnet  mathscinet  isi
14. 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  mathnet  mathscinet  zmath  isi
15. Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel”, SIGMA, 3 (2007), 060, 31 pp.  mathnet  mathscinet  zmath  isi  scopus
16. 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”, Tr. Mat. Inst. Steklova, 258 (2007),  162–184  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 258 (2007), 155–177  elib  scopus
17. A. N. Varchenko, “Bethe ansatz for arrangements of hyperplanes and the Gaudin model”, Mosc. Math. J., 6:1 (2006),  195–210  mathnet  mathscinet  zmath  isi
18. 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  mathnet  mathscinet  zmath  isi
19. 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  mathnet  mathscinet  zmath  isi
20. 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  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 131:1 (2005), 5270–5274
21. V. O. Tarasov, A. N. Varchenko, “Small elliptic quantum group $e_{\tau,\gamma}(\mathfrak{sl}_N)$”, Mosc. Math. J., 1:2 (2001),  243–286  mathnet  mathscinet  zmath  isi
22. A. N. Varchenko, G. Felder, “Algebraic Integrability of the Two-Body Ruijsenaars Operator”, Funktsional. Anal. i Prilozhen., 32:2 (1998),  8–25  mathnet  mathscinet  zmath; Funct. Anal. Appl., 32:2 (1998), 81–92  isi
23. 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  mathnet  mathscinet  zmath; St. Petersburg Math. J., 6:2 (1995), 275–313
24. A. N. Varchenko, “Combinatorics of a partial fraction decomposition”, Trudy Mat. Inst. Steklov., 193 (1992),  49–52  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 193 (1993), 51–55
25. A. N. Varchenko, “Determinant formula for Selberg-type integrals”, Funktsional. Anal. i Prilozhen., 25:4 (1991),  88–89  mathnet  mathscinet  zmath; Funct. Anal. Appl., 25:4 (1991), 304–305  isi
26. 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  mathnet  mathscinet  zmath; Leningrad Math. J., 2:3 (1991), 523–576
27. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 36:1 (1991), 155–167
28. A. N. Varchenko, “The determinant of a matrix of multidimensional hypergeometric integrals”, Dokl. Akad. Nauk SSSR, 308:4 (1989),  777–780  mathnet  mathscinet  zmath; Dokl. Math., 40:2 (1990), 359–362
29. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 35:3 (1990), 543–571
30. A. N. Varchenko, “Critical values and the determinant of the periods”, Uspekhi Mat. Nauk, 44:4(268) (1989),  235–236  mathnet  mathscinet  zmath; Russian Math. Surveys, 44:4 (1989), 209–210  isi
31. A. N. Varchenko, “The numbers of faces of a configuration of hyperplanes”, Dokl. Akad. Nauk SSSR, 302:3 (1988),  527–530  mathnet  mathscinet  zmath; Dokl. Math., 38:2 (1989), 291–295
32. 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  mathnet  mathscinet  zmath; J. Soviet Math., 52:4 (1990), 3305–3325
33. A. N. Varchenko, “Functional equations for a volume map”, Mat. Zametki, 44:4 (1988),  417–427  mathnet  mathscinet  zmath; Math. Notes, 44:4 (1988), 707–712  isi
34. A. N. Varchenko, I. M. Gel'fand, “Heaviside functions of a configuration of hyperplanes”, Funktsional. Anal. i Prilozhen., 21:4 (1987),  1–18  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:4 (1987), 255–270  isi
35. A. N. Varchenko, “Combinatorics and topology of the disposition of affine hyperplanes in real space”, Funktsional. Anal. i Prilozhen., 21:1 (1987),  11–22  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:1 (1988), 9–19  isi
36. A. N. Varchenko, “On normal forms of nonsmoothness of solutions of hyperbolic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987),  652–665  mathnet  mathscinet  zmath; Math. USSR-Izv., 30:3 (1988), 615–628
37. A. N. Varchenko, “The period map and the discriminant”, Mat. Sb. (N.S.), 134(176):1(9) (1987),  66–81  mathnet  mathscinet  zmath; Math. USSR-Sb., 62:1 (1989), 65–81
38. 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  mathnet  mathscinet  zmath
39. A. N. Varchenko, “Local classification of volume forms in the presence of a hypersurface”, Funktsional. Anal. i Prilozhen., 19:4 (1985),  23–31  mathnet  mathscinet  zmath; Funct. Anal. Appl., 19:4 (1985), 269–276  isi
40. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 26:1 (1986), 31–52
41. A. N. Varchenko, S. V. Chmutov, “On the tangent cone to the stratum $\mu=\operatorname{const}$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, 1,  6–9  mathnet  mathscinet  zmath
42. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 18:3 (1984), 171–183  isi
43. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 18:2 (1984), 98–108  isi
44. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 39:2 (1984), 209–210  isi
45. 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  mathnet  mathscinet  zmath
46. A. N. Varchenko, “The spectrum and decompositions of a critical point of a function”, Dokl. Akad. Nauk SSSR, 270:2 (1983),  267–270  mathnet  mathscinet  zmath
47. A. N. Varchenko, “Semicontinuity of the complex singularity index”, Funktsional. Anal. i Prilozhen., 17:4 (1983),  77–78  mathnet  mathscinet  zmath; Funct. Anal. Appl., 17:4 (1983), 307–309  isi
48. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 17:2 (1983), 79–83  isi
49. A. N. Varchenko, “Asymptotic behaviors of integrals, and Hodge structures”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 22 (1983),  130–166  mathnet  mathscinet  zmath; J. Soviet Math., 27:3 (1984), 2760–2784
50. A. N. Varchenko, A. B. Givental', “Mapping of periods and intersection form”, Funktsional. Anal. i Prilozhen., 16:2 (1982),  7–20  mathnet  mathscinet  zmath; Funct. Anal. Appl., 16:2 (1982), 83–93  isi
51. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 16:1 (1982), 1–9  isi
52. A. N. Varchenko, “On the number of integral points in a domain”, Uspekhi Mat. Nauk, 37:3(225) (1982),  177–178  mathnet  mathscinet  zmath; Russian Math. Surveys, 37:3 (1982), 223–224
53. 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, 6,  28–31  mathnet  mathscinet  zmath
54. 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  mathnet  mathscinet  zmath
55. A. N. Varchenko, “Asymptotic Hodge structure in the vanishing cohomology”, Izv. Akad. Nauk SSSR Ser. Mat., 45:3 (1981),  540–591  mathnet  mathscinet  zmath; Math. USSR-Izv., 18:3 (1982), 469–512
56. A. N. Varchenko, “Obstructions to local equivalence of distributions”, Mat. Zametki, 29:6 (1981),  939–947  mathnet  mathscinet  zmath; Math. Notes, 29:6 (1981), 479–484  isi
57. A. N. Varchenko, “The asymptotics of holomorphic forms determine a mixed Hodge structure”, Dokl. Akad. Nauk SSSR, 255:5 (1980),  1035–1038  mathnet  mathscinet  zmath
58. A. N. Varchenko, “Hodge properties of Gauss–Manin connectivities”, Funktsional. Anal. i Prilozhen., 14:1 (1980),  46–47  mathnet  mathscinet  zmath; Funct. Anal. Appl., 14:1 (1980), 36–37
59. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 13:1 (1979), 52–53
60. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 33:6 (1978), 263–264
61. 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  mathnet  mathscinet  zmath
62. A. N. Varchenko, “Newton polyhedra and estimation of oscillating integrals”, Funktsional. Anal. i Prilozhen., 10:3 (1976),  13–38  mathnet  mathscinet  zmath; Funct. Anal. Appl., 10:3 (1976), 175–196
63. A. N. Varchenko, “A theorem on topological versal deformation”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975),  294–314  mathnet  mathscinet  zmath; Math. USSR-Izv., 9:2 (1975), 277–296
64. A. N. Varchenko, “Local topological properties of differentiable mappings”, Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974),  1037–1090  mathnet  mathscinet  zmath; Math. USSR-Izv., 8:5 (1974), 1033–1082
65. A. N. Varchenko, “The relation between topological and algebro-geometric equisingularities according to Zariski”, Funktsional. Anal. i Prilozhen., 7:2 (1973),  1–5  mathnet  mathscinet  zmath; Funct. Anal. Appl., 7:2 (1973), 87–90
66. A. N. Varchenko, “Local topological properties of analytic mappings”, Izv. Akad. Nauk SSSR Ser. Mat., 37:4 (1973),  883–916  mathnet  mathscinet  zmath; Math. USSR-Izv., 7:4 (1973), 883–917
67. 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  mathnet  mathscinet  zmath
68. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 6:3 (1972), 225–227
69. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 6:5 (1972), 949–1008
70. A. N. Varchenko, “A theorem on the equisingularity of families of algebraic varieties”, Uspekhi Mat. Nauk, 26:1(157) (1971),  217–218  mathnet  mathscinet  zmath
71. A. N. Varchenko, “On the bifurcation of multiple integrals depending on a parameter”, Funktsional. Anal. i Prilozhen., 3:4 (1969),  79–80  mathnet  mathscinet  zmath; Funct. Anal. Appl., 3:4 (1969), 322–324

72. 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  mathnet  elib; Trans. Moscow Math. Soc., 72 (2011), viii–xi
73. 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  mathnet
74. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 64:3 (2009), 561–566  isi
75. 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”, Tr. Mat. Inst. Steklova, 259 (2007),  5–9  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 259 (2007), 1–5  elib  scopus
76. 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  mathnet
77. 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  mathnet
78. 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  mathnet

Presentations in Math-Net.Ru
1. Real algebraic geometry and integrable systems. Lecture 3
A. N. Varchenko
Summer School on Geometry and Mathematical Physics 2012
June 27, 2012 11:20   
2. Real algebraic geometry and integrable systems. Lecture 2
A. N. Varchenko
Summer School on Geometry and Mathematical Physics 2012
June 26, 2012 09:40   
3. Real algebraic geometry and integrable systems. Lecture 1
A. N. Varchenko
Summer School on Geometry and Mathematical Physics 2012
June 25, 2012 14:30   

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