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Varchenko, Aleksandr Nikolaevich

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Total publications: 68
Scientific articles: 61
Presentations: 3

Number of views:
This page:2976
Abstract pages:20057
Full texts:6138
References:1573
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Website: http://www.math.unc.edu/Faculty/av/

http://www.mathnet.ru/eng/person21441
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http://zbmath.org/authors/?q=ai:varchenko.alexander-n
https://mathscinet.ams.org/mathscinet/MRAuthorID/190269

Publications in Math-Net.Ru
2018
1. Giovanni Felder, Richárd Rimányi, Alexander Varchenko, “Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology”, SIGMA, 14 (2018), 132, 41 pp.  mathnet  isi
2017
2. 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
2015
3. Alexander Varchenko, Charles A. S. Young, “Populations of Solutions to Cyclotomic Bethe Equations”, SIGMA, 11 (2015), 091, 41 pp.  mathnet  isi  scopus
2013
4. Vitaly Tarasov, Alexander Varchenko, “Combinatorial Formulae for Nested Bethe Vectors”, SIGMA, 9 (2013), 048, 28 pp.  mathnet  mathscinet  isi  scopus
2012
5. 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
2011
6. 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
7. Richárd Rimányi, Vadim Schechtman, Alexander Varchenko, “Conformal blocks and equivariant cohomology”, Mosc. Math. J., 11:3 (2011),  561–581  mathnet  mathscinet  isi
8. Alexander Varchenko, “Quantum Integrable Model of an Arrangement of Hyperplanes”, SIGMA, 7 (2011), 032, 55 pp.  mathnet  mathscinet  isi  scopus
2010
9. 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
10. 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
2007
11. 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
12. 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
13. 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; Proc. Steklov Inst. Math., 258 (2007), 155–177  scopus
2006
14. A. N. Varchenko, “Bethe ansatz for arrangements of hyperplanes and the Gaudin model”, Mosc. Math. J., 6:1 (2006),  195–210  mathnet  mathscinet  zmath
2003
15. 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
16. 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
17. 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
2001
18. 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
1998
19. 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
1994
20. 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
1992
21. 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
1991
22. 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
1990
23. 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
24. 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
1989
25. 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
26. 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
1988
27. 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
28. 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
1987
29. 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
30. 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
31. 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
32. 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
1985
33. 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
34. 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
1984
35. 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
36. 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
37. 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
1983
38. 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
39. 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
40. 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
1982
41. 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
42. 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
43. 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
1981
44. 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
45. 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
46. 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
1980
47. 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
48. 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
1979
49. 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
1978
50. 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
1977
51. 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
1976
52. 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
1975
53. 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
1974
54. 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
1973
55. 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
56. 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
57. 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
1972
58. 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
59. 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
1971
60. 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
1969
61. 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

2011
62. 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
2010
63. 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
2009
64. 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
2007
65. 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; Proc. Steklov Inst. Math., 259 (2007), 1–5  scopus
1988
66. 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
1982
67. 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
1978
68. 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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