Full list of publications: |
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Citations (Crossref Cited-By Service + Math-Net.Ru) |
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1. |
A. Gorsky, I. Krichever, A. Marshakov, A. Mironov, A. Morozov, “Integrability and Seiberg–Witten exact solution”, Phys. Lett. B, 355:3-4 (1995), 466–474
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391
[x]
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2. |
I. M. Krichever, “Methods of algebraic geometry in the theory of non-linear equations”, Russian Math. Surveys, 32:6 (1977), 185–213 |
3. |
I. M. Krichever, “The $\tau$-function of the universal Whitham hierarchy, matrix models and topological field theories”, Comm. Pure Appl. Math., 47:4 (1994), 437–475 ; (1992), 34 pp., arXiv: hep-th/9205110
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320
[x]
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4. |
I. M. Krichever, “Integration of nonlinear equations by the methods of algebraic geometry”, Funct. Anal. Appl., 11:1 (1977), 12–26 |
5. |
I. M. Krichever, “Elliptic solutions of the Kadomtsev–Petviashvili equation and integrable systems of particles”, Funct. Anal. Appl., 14:4 (1980), 282–290 |
6. |
I. M. Krichever, S. P. Novikov, “Holomorphic bundles over algebraic curves and non-linear equations”, Russian Math. Surveys, 35:6 (1980), 53–79 |
7. |
I. Krichever, O. Lipan, P. Wiegmann, A. Zabrodin, “Quantum integrable models and discrete classical Hirota equations”, Commun. Math. Phys., 188:2 (1997), 267–304
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187
[x]
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8. |
I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funct. Anal. Appl., 22:3 (1988), 200–213 |
9. |
I. M. Krichever, S. P. Novikov, “Algebras of virasoro type, riemann surfaces and structures of the theory of solitons”, Funct. Anal. Appl., 21:2 (1987), 126–142 |
10. |
I. M. Krichever, “Rational solutions of the Kadomtsev–Petviashvili equation and integrable systems of $N$ particles on a line”, Funct. Anal. Appl., 12:1 (1978), 59–61 |
11. |
I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225 |
12. |
I. M. Krichever, “Commutative rings of ordinary linear differential operators”, Funct. Anal. Appl., 12:3 (1978), 175–185 |
13. |
I. M. Krichever, “Algebraic curves and non-linear difference equations”, Russian Math. Surveys, 33:4 (1978), 255–256 |
14. |
I. M. Krichever, A. V. Zabrodin, “Spin generalization of the Ruijsenaars–Schneider model, the non-Abelian Toda chain, and representations of the Sklyanin algebra”, Russian Math. Surveys, 50:6 (1995), 1101–1150 |
15. |
B. A. Dubrovin, I. M. Krichever, S. P. Novikov, “Integrable systems. I”, Dynamical systems – 4, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 4, VINITI, Moscow, 1985, 179–277 |
16. |
I. M. Krichever, D. H. Phong, “On the integrable geometry of soliton equations and $N=2$ supersymmetric gauge theories”, J. Differential Geom., 45:2 (1997), 349–389 ; (1996), 38 pp., arXiv: hep-th/9604199
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69
[x]
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17. |
I. Krichever, “Vector bundles and Lax equations on algebraic curves”, Comm. Math. Phys., 229:2 (2002), 229–269 ; (2001), 42 pp., arXiv: hep-th/0108110
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68
[x]
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18. |
B. A. Dubrovin, I. M. Krichever, S. P. Novikov, “The Schrödinger equation in a periodic field and Riemann surfaces”, Dokl. Akad. Nauk SSSR, 229:1 (1976), 15–18 |
19. |
I. M. Krichever, S. P. Novikov, “Virasoro-type algebras, Riemann surfaces and strings in Minkowsky space”, Funct. Anal. Appl., 21:4 (1987), 294–307 |
20. |
I. M. Krichever, “Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations”, Funct. Anal. Appl., 31:1 (1997), 25–39 |
21. |
I. M. Krichever, S. P. Novikov, “Algebras of virasoro type, energy-momentum tensor, and decomposition operators on Riemann surfaces”, Funct. Anal. Appl., 23:1 (1989), 19–33 |
22. |
I. M. Krichever, “Generalized elliptic genera and Baker–Akhiezer functions”, Math. Notes, 47:2 (1990), 132–142 |
23. |
I. M. Krichever, “Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations”, Mosc. Math. J., 2:4 (2002), 717–752
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45
[x]
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24. |
I. M. Krichever, “Baxter's equations and algebraic geometry”, Funct. Anal. Appl., 15:2 (1981), 92–103 |
25. |
I. Krichever, P. Wiegmann, A. Zabrodin, “Elliptic solutions to difference non-linear equations and related many-body problems”, Commun. Math. Phys., 193:2 (1998), 373–396
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40
[x]
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26. |
I. M. Krichever, S. P. Novikov, “Holomorphic bundles over Riemann surfaces and the Kadomtsev–Petviashvili equation. I”, Funct. Anal. Appl., 12:4 (1978), 276–286 |
27. |
I. M. Krichever, “Algebraic-geometric construction of the Zakharov–Shabat equations and their periodic solutions”, Dokl. Akad. Nauk SSSR, 227:2 (1976), 291–294 |
28. |
S. Yu. Dobrokhotov, I. M. Krichever, “Multi-phase solutions of the Benjamin–Ono equation and their averaging”, Math. Notes, 49:6 (1991), 583–594 |
29. |
I. M. Krichever, “Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model”, Funct. Anal. Appl., 20:3 (1986), 203–214 |
30. |
I. M. Krichever, “Nonlinear equations and elliptic curves”, J. Soviet Math., 28:1 (1985), 51–90 |
31. |
I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510 |
32. |
I. M. Krichever, “Self-similar solutions of equations of Korteweg -de Vries type”, Funct. Anal. Appl., 14:3 (1980), 234–236 |
33. |
I. M. Krichever, “General Rational Reductions of the KP Hierarchy and Their Symmetries”, Funct. Anal. Appl., 29:2 (1995), 75–80 |
34. |
I. M. Krichever, “Potentials with zero coefficient of reflection on a background of finite-zone potentials”, Funct. Anal. Appl., 9:2 (1975), 161–163 |
35. |
A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “Discrete Analogs of the Darboux–Egorov Metrics”, Proc. Steklov Inst. Math., 225 (1999), 16–39 |
36. |
I. M. Krichever, “Algebraic curves and commuting matricial differential operators”, Funct. Anal. Appl., 10:2 (1976), 144–146 |
37. |
I. Krichever, “Elliptic analog of the Toda lattice”, Int. Math. Res. Notices, 2000:8 (2000), 383–412
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22
[x]
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38. |
I. M. Krichever, “Two-Dimensional Algebraic-Geometric Operators with Self-Consistent Potentials”, Funct. Anal. Appl., 28:1 (1994), 21–32 |
39. |
I. M. Krichever, O. K. Sheinman, “Lax Operator Algebras”, Funct. Anal. Appl., 41:4 (2007), 284–294 |
40. |
A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “Elliptic Families of Solutions of the Kadomtsev–Petviashvili Equation and the Field Elliptic Calogero–Moser System”, Funct. Anal. Appl., 36:4 (2002), 253–266 |
41. |
I. M. Krichever, “Formal groups and the Atiyah–Hirzebruch formula”, Math. USSR-Izv., 8:6 (1974), 1271–1285 |
42. |
S. Grushevsky, I. Krichever, “The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces”, Geometry of Riemann surfaces and their moduli spaces, Surv. Differ. Geom., 14, Int. Press, Somerville, MA, 2009, 111–129
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18
[x]
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43. |
V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78 |
44. |
I. M. Krichever, “Analytic theory of difference equations with rational and elliptic coefficients and the Riemann–Hilbert problem”, Russian Math. Surveys, 59:6 (2004), 1117–1154 |
45. |
I. M. Krichever, “On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line”, J. Soviet Math., 21:3 (1983), 335–345 |
46. |
I. M. Krichever, “An analogue of d'Alembert's formula for the equations of the principal chiral field and for the Sine-Gordon equation”, Sov. Math., Dokl., 22 (1980), 79–84 |
47. |
S. Grushevsky, I. Krichever, “Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants”, Duke Math. J., 152:2 (2010), 317–371
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14
[x]
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48. |
I. M. Krichever, S. P. Novikov, “Trivalent graphs and solitons”, Russian Math. Surveys, 54:6 (1999), 1248–1249 |
49. |
I. M. Krichever, “Commuting Difference Operators and the Combinatorial Gale Transform”, Funct. Anal. Appl., 49:3 (2015), 175–188 |
50. |
I. M. Krichever, S. P. Novikov, “Holomorphic bundles and commuting difference operators. Two-point constructions”, Russian Math. Surveys, 55:3 (2000), 586–588 |
51. |
A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “A generating formula for solutions of the associativity equations”, Russian Math. Surveys, 54:2 (1999), 427–429 |
52. |
I. M. Krichever, S. P. Novikov, “Holomorphic fiberings and nonlinear equations. Finite zone solutions of rank 2”, Dokl. Akad. Nauk SSSR, 247:1 (1979), 33–37 |
53. |
V. V. Avilov, I. M. Krichever, S. P. Novikov, “Evolution of the Whitham zone in the Korteweg–de Vries theory”, Dokl. Akad. Nauk SSSR, 295:2 (1987), 345–349 |
54. |
I. M. Krichever, “Two-dimensional periodic difference operators and algebraic geometry”, Dokl. Akad. Nauk SSSR, 285:1 (1985), 31–36 |
55. |
I. M. Krichever, “Obstructions to the existence of $S^1$-actions. Bordism of ramified coverings”, Math. USSR-Izv., 10:4 (1976), 783–797 |
56. |
I. M. Krichever, S. P. Novikov, “Holomorphic bundles and scalar difference operators: one-point constructions”, Russian Math. Surveys, 55:1 (2000), 180–181 |
57. |
V. M. Buchstaber, I. M. Krichever, “Vector addition theorems and Baker–Akhiezer functions”, Theoret. and Math. Phys., 94:2 (1993), 142–149 |
58. |
I. M. Krichever, “The Peierls model”, Funct. Anal. Appl., 16:4 (1982), 248–263 |
59. |
I. M. Krichever, “The laplace method, algebraic curves, and nonlinear equations”, Funct. Anal. Appl., 18:3 (1984), 210–223 |
60. |
I. Krichever, “Real-normalized differentials and the elliptic Calogero-Moser system”, Complex geometry and dynamics, Abel Symp., 10, Springer, Cham, 2015, 123–137
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5
[x]
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61. |
I. M. Krichever, ““Hessians” of integrals of the Korteweg–de Vries equation and perturbations of finite-zone solutions”, Dokl. Akad. Nauk SSSR, 270:6 (1983), 1312–1317 |
62. |
I. M. Krichever, “Real Normalized Differentials and Arbarello's Conjecture”, Funct. Anal. Appl., 46:2 (2012), 110–120 |
63. |
I. Krichever, O. Lipan, P. Wiegmann, A. Zabrodin, “Quantum integrable systems and elliptic solutions of classical discrete nonlinear equations”, Low-Dimensional Applications of Quantum Field Theory, NATO ASI Series, 361, Springer, Boston, 1997, 279–317
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4
[x]
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64. |
S. Grushevsky, I. M. Krichever, Ch. Norton, “Real-normalized differentials: limits on stable curves”, Russian Math. Surveys, 74:2 (2019), 265–324 |
65. |
S. M. Gusein-Zade, I. M. Krichever, “Formulae for the fixed points of an action of the group $Z_p$”, Uspekhi Mat. Nauk, 28:1(169) (1973), 237–238 |
66. |
I. M. Krichever, “Actions of finite cyclic groups on quasicomplex manifolds”, Math. USSR-Sb., 19:2 (1973), 305–319 |
67. |
A. V. Il'ina, I. M. Krichever, “Triangular Reductions of the $2D$ Toda Hierarchy”, Funct. Anal. Appl., 51:1 (2017), 48–65 |
68. |
I. M. Krichever, “Rational solutions of the duality equations for Yang–Mills fields”, Funct. Anal. Appl., 13:4 (1979), 303–305 |
69. |
I. M. Krichever, “Equivariant Hirzebruch genera. The Atiyah–Hirzebruch formula”, Uspekhi Mat. Nauk, 30:1(181) (1975), 243–244 |
70. |
I. M. Krichever, “Remark on the paper “Actions of finite cyclic groups on quasicomplex manifolds””, Math. USSR-Sb., 24:1 (1974), 145–146 |
71. |
I. M. Krichever, A. V. Iljina, N. A. Nekrasov, Funktsional. Anal. i Prilozhen. |
72. |
I. M. Krichever, “Abelian solutions of the soliton equations and Riemann–Schottky problems”, Russian Math. Surveys, 63:6 (2008), 1011–1022 |
73. |
I. M. Krichever, “Bordisms of groups acting freely on spheres”, Uspekhi Mat. Nauk, 26:6(162) (1971), 245–246 |
74. |
Igor Krichever, Nikita Nekrasov, “Novikov–Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model”, SIGMA, 18 (2022), 6 , 37 pp., arXiv: 2106.14201 ; |
75. |
I. Krichever, A. Varchenko, Incarnations of $XXX$ $\widehat{\frak{sl}_N}$ Bethe ansatz equations and integrable hierarchies, 2019, 57 pp., arXiv: 1907.12198 |
76. |
I. Krichever, “Integrable chains on algebraic curves”, Geometry, Topology, and Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 212, eds. V.M. Buchstaber, I.M. Krichever, AMS, 2004, 219–236; 2003, arXiv: hep-th/0309255 |
77. |
I. Krichever, K. Vaninsky, “The periodic and open Toda lattice”, Mirror Symmetry IV, AMS/IP Studies in Advanced Mathematics, 33, eds. Eric D'Hoker et al., 2002, 139–158; 2000, arXiv: hep-th/0010184 |
78. |
I. Krichever, A. Zabrodin, “Vacuum curves of elliptic L-operators and representations of Sklyanin algebra”, Translations of American Mathematical Society, Advances in the Mathematical Sciences, Series 2, 191, eds. A. Yu. Morozov, M. A. Olshanetsky, Providence, Rhode Island, 1999, 199–222; 1998, arXiv: solv-int/9801022 |
79. |
I. Krichever, O. Babelon, E. Billey, M. Talon, “Spin generalization of the Calogero-Moser system and the matrix KP equation”, Amer. Math. Soc. Transl. Ser. 2, 170 (1995), 83–119; (1994), arXiv: hep-th/9411160 |
80. |
I. M. Krichever, “A periodic problem for the Kadomtsev–Petviashvili equation”, Dokl. Math., 37:1 (1988), 157–161 |
81. |
I. E. Dzyaloshinskii, I. M. Krichever, Ya. Khronek, “Novyi metod nakhozhdeniya dinamicheskikh reshenii v modeli Paierlsa”, ZhETF, 94:7 (1988), 344–354 |
82. |
B.A. Dubrovin, I.M. Krichever, T.M. Malanyuk, V.G. Makhankov, “Tochnye resheniya nestatsionarnogo uravneniya Shredingera s samosoglasovannymi potentsialami”, Fizika element. chastits i atom. yadra, 19:3 (1988), 579–621 |
83. |
V. M. Eleonskii, I. M. Krichever, N. E. Kulagin, “Rational multisoliton solutions of the nonlinear Schrödinger equation”, Dokl. Akad. Nauk SSSR, 287:3 (1986), 606–610 |
84. |
I.E. Dzyaloshinskii, I.M. Krichever, “Sound and charge-density wave in the discrete Peierls model”, Sov. Phys. JETP, 58:5 (1983), 1031–1040 |
85. |
I. M. Krichever, “Algebro-geometric spectral theory of the Schrödinger difference operator and the Peierls model”, Dokl. Akad. Nauk SSSR, 265:5 (1982), 1054–1058 |
86. |
S.A. Brazovskii, N.E. Dzyaloshinskii, I.M. Krichever, “Discrete Peierls models with exact solutions”, Sov. Phys. JETP, 56:1 (1982), 212–225 |
87. |
I.E. Dzyaloshinskii, I.M. Krichever, “Commensurability effects in the discrete Peierls model”, Sov. Phys. JETP, 56:4 (1982), 908–913 |
88. |
S.A. Brazovskii, I.E. Dzyaloshinskii, I.M. Krichever, “Exactly soluble Peierls models”, Phys. Lett. A, 91:1 (1982), 40–42 |
89. |
I.M. Krichever, “The periodic non-Abelian Toda chain and its two-dimensional generalization”, Appendix to the paper B A Dubrovin «Theta functions and non-linear equations», Russ. Math. Surv., 1981, 36, 11–92, Russian Math. Surveys, 36:2 (1981), 11–92 |
90. |
I. M. Krichever, “The invariance of characteristic classes for manifolds of the homotopy type of CP^n$”, Uspekhi Mat. Nauk, 28:5(173) (1973), 245–246 |
91. |
I. M. Krichever, L. A. Takhtadzhyan, “Algebraic de Rham theorem and Baker–Akhiezer function”, Izv. Math., 88:3 (2024), 506–514 |
92. |
I. Krichever, A. Zabrodin, “Monodromy free linear equations and many-body systems”, Lett. Math. Phys., 113 (2023), 75 , 36 pp. ; |
93. |
G. Fichera, Yu. M. Sukhov, N. P. Klepikov, I. M. Krichever, N. F. Morozov, S. I. Pokhozhaev, V. E. Zakharov, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 37:2(224) (1982), 255–262 |
94. |
A. M. Astashov, I. V. Astashova, A. V. Bocharov, V. M. Buchstaber, V. A. Vassiliev, A. Verbovetsky, A. M. Vershik, A. P. Veselov, M. M. Vinogradov, L. Vitagliano, R. F. Vitolo, Th. Th. Voronov, V. G. Kac, Y. Kosmann-Schwarzbach, I. S. Krasil'shchik, I. M. Krichever, A. P. Krishchenko, S. K. Lando, V. V. Lychagin, M. Marvan, V. P. Maslov, A. S. Mishchenko, S. P. Novikov, V. N. Rubtsov, A. V. Samokhin, A. B. Sossinsky, J. Stasheff, D. B. Fuchs, A. Ya. Khelemsky, N. G. Khor'kova, V. N. Chetverikov, A. S. Schwarz, “Alexandre Mikhailovich Vinogradov (obituary)”, Russian Math. Surveys, 75:2 (2020), 369–375 |
95. |
A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, A. N. Shiryaev, “Vladimir Antonovich Zorich (on his 80th birthday)”, Russian Math. Surveys, 73:5 (2018), 935–939 |
96. |
I. Ya. Aref'eva, V. E. Zakharov, V. V. Kozlov, I. M. Krichever, V. P. Maslov, S. P. Novikov, A. M. Polyakov, N. Yu. Reshetikhin, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, L. A. Takhtajan, S. L. Shatashvili, “Ludwig Dmitrievich Faddeev (obituary)”, Russian Math. Surveys, 72:6 (2017), 1157–1163 |
97. |
V. E. Adler, Yu. Yu. Berest, V. M. Buchstaber, P. G. Grinevich, B. A. Dubrovin, I. M. Krichever, S. P. Novikov, A. N. Sergeev, M. V. Feigin, J. Felder, E. V. Ferapontov, O. A. Chalykh, P. I. Etingof, “Alexander Petrovich Veselov (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1159–1176 |
98. |
A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590 |
99. |
V. Buchstaber, S. Gusein-Zade, Yu. Ilyashenko, A. Kirillov, I. Krichever, S. Natanzon, S. Novikov, A. Sergeev, A. Sossinsky, M. Tsfasman, “Oleg Sheinman”, Mosc. Math. J., 9:3 (2009), 723–724 |
100. |
V. M. Buchstaber, Yu. S. Ilyashenko, I. M. Krichever, O. K. Sheinman, A. B. Sossinski, M. A. Tsfasman, “Sergey Petrovich Novikov”, Mosc. Math. J., 3:4 (2003), 1206–1208 |
101. |
Yu. S. Ilyashenko, I. M. Krichever, S. P. Novikov, M. A. Tsfasman, V. A. Vassiliev, “Victor Buchstaber”, Mosc. Math. J., 3:1 (2003), 257 |
102. |
A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635 |
103. |
Yu. I. Manin, I. M. Krichever, S. P. Novikov, Ya. I. Belopol'skaya, Yu. L. Daletskii, O. I. Bogoyavlenskii, F. A. Berezin, E. S. Fradkin, E. A. Novikov, Yu. B. Sedov, A. E. Ordanovich, R. Finn, S. I. Andersson, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 33:5(203) (1978), 209–217 |
104. |
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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