igorkrichever

Igor Krichever

Professor, Director of Skoltech Center for Advanced Studies
Center for Advanced Studies

Igor M. Krichever is a mathematician with a prominent academic record. Several objects of contemporary mathematics bear his name: Krichever genus, Krichever–Novikov equation, Krichever–Novikov algebras, Krichever construction relating Baker–Akhieser functions to the Sato Grassmanian, as well as Buchstaber–Krichever functional equation.

Igor obtained his PhD from Lomonosov Moscow State University under the guidance of the distinguished Russian mathematician Sergei Petrovich Novikov, who until today remains Igor’s close collaborator. They have worked together on a number of joint projects and co-authored more than 20 works on integrable systems, string theory, algebraic geometry and topology methods in modern mathematical and theoretical physics.

Prior to joining Skoltech, Igor held senior research positions at Moscow Power Engineering Institute and the Institute for Problems in Mechanics, as well as faculty position at Moscow Independent University. He was also Deputy Director of the Kharkevich Institute of Information Transmission Problems.  Nowadays Igor is also a leading researcher of the Landau Institute for Theoretical Physics, RAS, a professor at the Higher School of Economics, Moscow, and at the Columbia University, where he also chaired the Mathematics Department from 2008 to 2011. Igor is contributing to the professional community worldwide by being a member of Executive Committees of the European Mathematical Society and editorial boards of professional journals, including Functional analysis and its applications, International Mathematical Research Notes, and Russian Mathematical Surveys.

    1. Real normalized differentials and compact cycles in the moduli space of curves. (PDF: English, arXiv: 1204.2192)
    2. Real normalized differentials and Arbarello’s conjecture. (PDF: English, arXiv:1112.6427)
    3. Soliton equations and the Riemann-Schottky problem. (PDF: English, arXiv: 1111.0164)
      (with T. Shiota).
    4. Foliations on the moduli space of curves, vanishing in cohomology, and Calogero-Moser curves. (PDF: English, arXiv: 1108.4211)
      (with S. Grushevsky).
    5. A note on critical points of integrals of soliton equations. (PDF: English, arXiv:1005.3741)
      Anal. Math. Phys. 1:1 (2011), 15–35 (with D. Zakharov).
    6. Abelian solutions of the soliton equations and geometry of abelian varieties. (PDF:English, arXiv: 0804.0794)
      Liaison, Schottky problem and invariant theory, Progr. Math. 280 (2010), 197–222 (with T. Shiota).
    7. Characterizing Jacobians via trisecants of the Kummer Variety. (PDF: English, arXiv:math/0605625)
      Ann. of Math. (2) 172:1 (2010), 485–516 .
    8. Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants. (PDF: English, arXiv: 0705.2829)
      Duke Math. J. 152:2 (2010), 317–371 (with S. Grushevsky).
    1. The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces. (PDF: English, arXiv: 0810.2139)
      Surv. Differ. Geom. 14 (2009), 111–129 (with S. Grushevsky).
    2. Abelian solutions of the soliton equations and Riemann-Schottky problems. (PDF:English)
      Uspekhi Mat. Nauk 63:6(384) (2008), 19–30 .
    3. Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons. (PDF: English, arXiv: hep-th/0212313)
      Superstring theory, Adv. Lect. Math. (ALM) 1 (2008), 124–177 (with E. D’Hoker and D.H. Phong).
    4. Abelian solutions of the KP equation. (PDF: English, arXiv: 0804.0274)
      Geometry, topology, and mathematical physics, Amer. Math. Soc. Transl. Ser. 2 224 (2008), 173–191 (with T. Shiota).
    5. On the scaling limit of a singular integral operator. (PDF: English, arXiv: 0708.4157)
      Geom. Dedicata 132 (2008), 121–134 (with D.H. Phong).
    6. Lax operator algebras. (PDF: Russian, English, arXiv: math/0701648)
      Funktsional. Anal. i Prilozhen. 41:4 (2007), 46–59 (with O.K. Sheinman).
    7. A characterization of Prym varieties. (PDF: English, arXiv: math/0506238)
      Int. Math. Res. Not. Art. ID 81476 (2006), 36pp .
    8. Integrable equations, addition theorems, and the Riemann-Schottky problem. (PDF: Russian, English)
      Uspekhi Mat. Nauk 61:1 (2006), 25–84 (with V.M. Bukhshtaber).
    9. Integrable linear equations and the Riemann-Schottky problem. (PDF: English, arXiv:math/0504192)
      Algebraic geometry and number theory, Progr. Math. 253 (2006), 497–514 .
    10. Conformal mappings and the Whitham equations. (PDF: English)
      Surveys in modern mathematics, London Math. Soc. Lecture Note Ser. Cambridge Univ. Press(2005), 316–327 .
    11. Characterizing Jacobians via flexes of the Kummer Variety. (PDF: English, arXiv:math/0502138)
      Math. Res. Lett. 13:1 (2006), 109–123 (with E. Arbarello and G. Marini).
    12. Algebraic versus Liouville integrability of the soliton systems. (PDF: English)
      XIVth International Congress on Mathematical Physics World Sci. Publ (2005), 50–67 .
    13. Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains. (PDF: English, arXiv: hep-th/0309010)
      Comm. Math. Phys. 259:1 (2005), 1–44 (with A. Marshakov and A. Zabrodin).
    1. Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem. (PDF: Russian, English, arXiv: math-ph/0407018)
      Uspekhi Mat. Nauk 59:6 (2004), 111–150 .
    2. Laplacian growth and Whitham equations of soliton theory. (PDF: English, arXiv:nlin/0311005)
      Phys. D 198:1–2 (2004), 1–28 (with M. Mineev-Weinstein, P. Wiegmann, and A. Zabrodin).
    3. Integrable chains on algebraic curves. (PDF: English, arXiv: hep-th/0309255)
      Geometry, topology, and mathematical physics, Amer. Math. Soc. Transl. Ser. 2 212 (2004), 219–236 .
    4. A two-dimensionalized Toda chain, commuting difference operators, and holomorphic vector bundles. (PDF: Russian, English, arXiv: math-ph/0308019)
      Uspekhi Mat. Nauk 58:3 (2003), 51–88 (with S.P. Novikov).
    5. Elliptic families of solutions of the Kadomtsev-Petviashvili equation, and the field analogue of the elliptic Calogero-Moser system. (PDF: Russian, English, arXiv: hep-th/0203192)
      Funktsional. Anal. i Prilozhen. 36:4 (2002), 1–17 (with A.A. Akhmetshin and Yu.S. Volvovski).
    6. Spin chains with twisted monodromy. (PDF: English, arXiv: hep-th/0110098)
      J. Inst. Math. Jussieu 1:3 (2002), 477–492 (with D.H. Phong).
    7. Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations. (PDF: English, arXiv: hep-th/0112096)
      Mosc. Math. J. 2:4 (2002), 717–752 .
    8. Vector bundles and Lax equations on algebraic curves. (PDF: English, arXiv: hep-th/0108110)
      Comm. Math. Phys. 229:2 (2002), 229–269 .
    9. The periodic and open Toda lattice. (PDF: English, arXiv: hep-th/0010184)
      Mirror symmetry, IV (Montreal, QC, 2000), AMS/IP Stud. Adv. Math. 33 (2002), 139–158 (with K.L. Vaninsky).
    10. The τ-function for analytic curves. (PDF: English, arXiv: hep-th/0005259)
      Random matrix models and their applications, Math. Sci. Res. Inst. Publ. 40 (2000), 285–299 (withI.K. Kostov, M. Mineev-Weinstein, P. Wiegmann, and A. Zabrodin).
    11. Holomorphic bundles and commuting difference operators. Two-term constructions. (PDF: Russian, English)
      Uspekhi Mat. Nauk 55:3(333) (2000), 181–182 (with S.P. Novikov).
    12. Holomorphic bundles and difference scalar operators: single-point constructions. (PDF: Russian, English, arXiv: math-ph/0004008)
      Uspekhi Mat. Nauk 55:1(331) (2000), 187–188 (with S.P. Novikov).
    13. Spin chain models with spectral curves from M theory. (PDF: English, arXiv: hep-th/9912180)
      Comm. Math. Phys. 213:3 (2000), 539–574 (with D.H. Phong).
    14. Elliptic analog of the Toda lattice. (PDF: English, arXiv: hep-th/9909224)
      Internat. Math. Res. Notices 8 (2000), 383–412 .
    15. Baker-Akhiezer functions and integrable systems.
      Integrability: The Seiberg-Witten and Whitham equations Gordon and Breach (2000), 1–22 .
    16. Elliptic solutions to difference nonlinear equations and nested Bethe ansatz equations. (PDF: English, arXiv: solv-int/9804016)
      Calogero-Moser-Sutherland models (Montréal, QC, 1997) CRM Ser. Math. Phys. Springer (2000),249–271 .
    1. Trivalent graphs and solitons. (PDF: Russian, English, arXiv: math-ph/0004009)
      Uspekhi Mat. Nauk 54:6(330) (1999), 149–150 (with S.P. Novikov).
    2. Periodic and almost-periodic potentials in inverse problems. (PDF: English, arXiv:math-ph/0003004)
      Inverse Problems 15:6 (1999), 117–144 (with S.P. Novikov).
    3. A generating formula for solutions of associativity equations. (PDF: Russian, English, arXiv: hep-th/9904028)
      Uspekhi Mat. Nauk 54:2(326) (1999), 167–168 (with A.A. Akhmetshin and Yu.S. Volvovski).
    4. Discrete analogues of the Darboux-Egorov metrics. (PDF: Russian, English, arXiv: hep-th/9905168)
      Tr. Mat. Inst. Steklova 255 (1999), 21–45 (with A.A. Akhmetshin and Yu.S. Volvovski).
    5. Vacuum curves of elliptic L-operators and representations of Sklyanin algebra. (PDF: English, arXiv: solv-int/9801022)
      Moscow Seminar in Mathematical Physics Amer. Math. Soc. Transl. Ser. 2 (1999), 199–221 (withA. Zabrodin).
    6. Symplectic forms in the theory of solitons. (PDF: English, arXiv: hep-th/9708170)
      Surveys in differential geometry: integral systems Int. Press, Boston, MA (1998), 239–313 (withD.H. Phong).
    7. Elliptic solutions to difference non-linear equations and related many-body problems. (PDF: English, arXiv: hep-th/9704090)
      Comm. Math. Phys. 193:2 (1998), 373–396 (with P. Wiegmann and A. Zabrodin).
    8. Solitons in high-energy QCD. (PDF: English, arXiv: hep-th/9704079)
      Nuclear Physics B 505:1–2 (1997), 387–414 (with G.P. Korchemsky).
    9. Algebraic-geometric n-orthogonal curvilinear coordinate systems and the solution of associativity equations. (PDF: Russian, English, arXiv: hep-th/9611158)
      Funktsional. Anal. i Prilozhen. 31:1 (1997), 32–50 .
    10. The renormalization group equation in N=2 supersymmetric gauge theories. (PDF:English, arXiv: hep-th/9610156)
      Nuclear Phys. B 494:1–2 (1997), 89–104 (with E. D’Hoker and D.H. Phong).
    11. The effective prepotential of N=2 supersymmetric SO(Nc) and Sp(Nc) gauge theories. (PDF: English, arXiv: hep-th/9609145)
      Nuclear Phys. B 489:1–2 (1997), 211–222 (with E. D’Hoker and D.H. Phong).
    12. The effective prepotential of N=2 supersymmetric SU(Nc) gauge theories. (PDF:English, arXiv: hep-th/9609041)
      Nuclear Phys. B 489:1–2 (1997), 197–210 (with E. D’Hoker and D.H. Phong).
    13. Quantum integrable models and discrete classical Hirota equations. (PDF: English)
      Comm. Math. Phys. 188:2 (1997), 267–304 (with O. Lipan, P. Wiegmann, and A. Zabrodin).
    14. On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories. (PDF: English, arXiv: hep-th/9604199)
      J. Differential Geom. 45:N2 (1997), 349–389 (with D.H. Phong).
    15. Quantum integrable systems and classical discrete nonlinear dynamics. (PDF:English, arXiv: hep-th/9604080)
      Statistical models, Yang-Baxter equation and related topics, and Symmetry, statistical mechanical models and applications (Tianjin, 1995) World Sci. Publ., River Edge, NJ (1996), 211–227 (withO. Lipan, P. Wiegmann, and A. Zabrodin).
    16. Multidimensional vector addition theorems and the Riemann theta functions. (PDF:English)
      Internat. Math. Res. Notices 10 (1996), 505–513 (with V. Buchstaber).
    17. Integrability and Seiberg-Witten exact solution. (PDF: English, arXiv: hep-th/9505035)
      Phys. Lett. B 355:3–4 (1995), 466–474 (with A. Gorsky, A. Marshakov, A. Mironov, and A. Morozov).
    18. Spin generalization of the Ruijsenaars-Schneider model, the non-Abelian 2D Toda chain, and representations of the Sklyanin algebra. (PDF: Russian, English, arXiv: hep-th/9505039)
      Uspekhi Mat. Nauk 50:6(306) (1995), 3–56 (with A. Zabrodin).
    19. Algebraic-geometrical methods in the theory of integrable equations and their perturbations. (PDF: English)
      Acta Appl. Math. 39:1–3 (1995), 93–125 .
    20. Linear operators with self-consistent coefficients and rational reductions of KP hierarchy. (PDF: English)
      Phys. D 87:1–4 (1995), 14–19 .
    21. Spin generalization of the Calogero-Moser system and the matrix KP equation. (PDF: English, arXiv: hep-th/9411160)
      Amer. Math. Soc. Transl. Ser. 2 170 (1995), 83–119 (with O. Babelon, E. Billey, M. Talon).
    22. Finite genus solutions to the Ablowitz-Ladik equations. (PDF: English)
      Comm. Pure Appl. Math. 48:12 (1995), 1369–1440 (with P.D Miller, N.M. Ercolani, and C.D. Levermore).
    23. General rational reductions of the Kadomtsev-Petviashvili hierarchy and their symmetries. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 29:2 (1995), 1–8 .
    1. Elliptic solutions of nonlinear integrable equations and related topics. (PDF:English)
      Acta Appl. Math. 36:1–2 (1994), 7–25 .
    2. Algebrogeometric two-dimensional operators with self-consistent potentials. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 28:1 (1994), 26–40 .
    3. The τ-function of the universal Whitham hierarchy, matrix models and topological field theories. (PDF: English, arXiv: hep-th/9205110)
      Comm. Pure Appl. Math. 47:4 (1994), 437–475 .
    4. Vector addition theorems and Baker-Akhiezer functions. (PDF: Russian, English)
      Teoret. Mat. Fiz. 94:2 (1993), 200–212 (with V.M. Bukhshtaber).
    5. The Cauchy problem for doubly periodic solutions of KP-II equation.
      Important developments in soliton theory Springer (1993), 123–146 .
    6. Perturbation Theory in Periodic Problems for Two-Dimensional Integrable Systems.
      Sov. Sci. Rev., Sect. C, Math. Phys. Rev. 9:2 (1992), 1–103 .
    7. Whitham theory for integrable systems and topological quantum field theories.
      New symmetry principles in quantum field theory (Cargèse, 1991) Plenum (1992), 309–327 .
    8. The dispersionless Lax equations and topological minimal models. (PDF: English)
      Comm. Math. Phys. 143:2 (1992), 415–429 .
    9. Multiphase solutions of the Benjamin-Ono equation and their averaging. (PDF:Russian, English)
      Mat. Zametki 49:6 (1991), 42–58 (with S.Yu. Dobrokhotov).
    10. The periodic problems for two-dimensional integrable systems.
      Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo (1991), 1353–1362 .
    11. The averaging procedure for the soliton-like solutions of integrable systems.
      Mechanics, analysis and geometry: 200 years after Lagrange North-Holland (1991), 99–125 .
    12. Riemann surfaces, operator fields, strings. Analogues of the Fourier-Laurent bases. (PDF: English)
      Physics and mathematics of strings World Scientific (1990), 356–388 (with S.P. Novikov).
    13. Generalized elliptic genera and Baker-Akhiezer functions. (PDF: Russian, English)
      Mat. Zametki 47:2 (1990), 34–45 .
    14. On Heisenberg relations for the ordinary linear differential operators.
      ETH Zürich preprint (1990) .

                   63.  Spectral theory of two-dimensional periodic operators and its applications. (PDF:Russian, EnglishUspekhi Mat. Nauk 44:2(266) (1989), 121–184 .

    1. Algebras of Virasoro type, the energy-momentum tensor, and operator expansions on Riemann surfaces. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 23:1 (1989), 24–40 (with S.P. Novikov).
    2. Algebraic-geometry methods in soliton theory.
      Soliton theory: a survey of results., Nonlinear Sci. Theory Appl., Chapter 14 (1990), 354–400 (withP.G. Grinevich).
    3. New method of finding dynamic solutions in the Peierls model. (PDF: English)
      Soviet Phys. JETP 94:7 (1988), 344–354 (with I.E. Dzyaloshinskii, J. Chronek).
    4. A periodic problem for the Kadomtsev-Petviashvili equation.
      Dokl. Akad. Nauk SSSR 298:4 (1988), 802–807 .
    5. Virasoro-Gelfand-Fuks type algebras, Riemann surfaces, operator’s theory of closed strings. (PDF: English)
      J. Geom. Phys. 5:4 (1988), 631–661 (with S.P. Novikov).
    6. Exact solutions of the time-dependent Schrödinger equation with self-consistent potentials. (PDF: Russian)
      Soviet J. Particles and Nuclei 19:3 (1988), 579–621 (with B.A. Dubrovin, T.M. Malanyuk, V.G. Makhan’kov).
    7. The averaging method for two-dimensional “integrable” equations. (PDF: Russian,English)
      Funktsional. Anal. i Prilozhen. 22:3 (1988), 37–52 .
    8. Evolution of the Whitham zone in the Korteweg-de Vries theory. (PDF: English)
      Dokl. Akad. Nauk SSSR 295:2 (1987), 345–349 (with V.V. Avilov, S.P. Novikov).
    9. Algebras of Virasoro type, Riemann surfaces and strings in Minkowski space. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 21:4 (1987), 47–61 (with S.P. Novikov).
    10. Algebras of Virasoro type, Riemann surfaces and the structures of soliton theory. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 21:2 (1987), 46–63 (with S.P. Novikov).
    11. The spectral theory of “finite-gap” nonstationary Schrödinger operators. The nonstationary Peierls model. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 20:3 (1986), 42–54 .
    12. Wess-Zumino Lagrangians in chiral models and quantization of their constants. (PDF: English)
      Nuclear Phys. B 264:2–3 (1986), 415–422 (with M.A. Olshanetsky, A.M. Perelomov).
    13. Rational multisoliton solutions of the nonlinear Schrödinger equation.
      Dokl. Akad. Nauk SSSR 287:3 (1986), 606–610 (with V.M. Eleonskii, N.E. Kulagin).
    14. Algebraic-geometrical methods in some problems of solid state physics.
      Proc. int. conf Dubna (1985) .
    15. Two-dimensional periodic Schrödinger operators and Prym’s θ-functions. (PDF:English)
      Geometry today (Rome, 1984), Progr. Math., 60 (1985), 283–301 (with A.P. Veselov, S.P. Novikov).
    16. Integrable systems. I. (PDF: Russian)
      Itogi Nauki i Tekhniki, Akad. Nauk SSSR, VINITI, Dynamical Systems 4 (1985), 179–277 (withB.A. Dubrovin, S.P. Novikov).
    17. Two-dimensional periodic difference operators and algebraic geometry.
      Dokl. Akad. Nauk SSSR 285:1 (1985), 31–36 .
    1. The Laplace method, algebraic curves and nonlinear equations. (PDF: Russian,English)
      Funktsional. Anal. i Prilozhen. 18:3 (1984), 43–56 .
    2. Nonlinear equations and elliptic curves. (PDF: Russian, English)
      Itogi Nauki i Tekhniki, Akad. Nauk SSSR, VINITI, 23 (1983), 79–136 .
    3. Sound and charge-density wave in the discrete Peierls model. (PDF: English)
      JETP 58:5 (1983), 1031–1040 (with I.E. Dzyaloshinskii).
    4. The “Hessian” of integrals of the Korteweg-de Vries equation and perturbations of finite-gap solutions.
      Dokl. Akad. Nauk SSSR 270:6 (1983), 1312–1317 .
    5. Algebraic geometry methods in the theory of the Baxter-Yang equations.
      Soviet Science Reviews, Math. Phys. Rev. 3 (1982), 53–81.
    6. Topological and algebraic-geometrical methods in contemporary mathematical physics.
      Soviet Science Reviews, Math. Phys. Rev. 3 (1982), 1–151 (with B.A. Dubrovin, S.P. Novikov).
    7. The Peierls model. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 16:4 (1982), 10–26 .
    8. Commensurability effects in the discrete Peierls model. (PDF: English)
      Soviet Phys. JETP 56:4 (1982), 908–913 (with I.E. Dzyaloshinskii).
    9. Exactly soluble Peierls models. (PDF: English)
      Phys. Let A 91:1 (1982), 40–42 (with S.A Brazovskii, I.E. Dzyaloshinskii).
    10. Discrete Peierls models with exact solutions. (PDF: English)
      Soviet Phys. JETP 56:1 (1982), 212–225 (with S.A Brazovskii, I.E. Dzyaloshinskii).
    11. Algebro-geometric spectral theory of the Schrödinger difference operator and the Peierls model.
      Dokl. Akad. Nauk SSSR 265:5 (1982), 1054–1058 .
    12. The spectral theory of difference operators, algebraic geometry, and Peierls model. (PDF: Russian)
      Uspekhi Mat. Nauk 37:2(224) (1982), 259–260 .
    13. Holomorphic bundles and nonlinear equations. (PDF: English)
      Physica D: Nonlinear Phenomena 3:1–2 (1981), 267–293 (with S.P. Novikov).
    14. The Baxter equations and algebraic geometry. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 15:2 (1981), 22–35 .
    15. The periodic non-Abelian Toda chain and its two-dimensional generalization. (PDF:Russian, English)
      Uspekhi Mat. Nauk 36:2(218) (1981), 72–77 .
    16. Elliptic solutions of the Kadomcev-Petviašvili equations, and integrable systems of particles. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 14:4 (1980), 45–54 .
    17. Holomorphic bundles over algebraic curves, and nonlinear equations. (PDF: Russian,English)
      Uspekhi Mat. Nauk 35:6(216) (1980), 47–68 (with S.P. Novikov).
    18. Self-similar solutions of equations of Korteweg-de Vries type. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 14:3 (1980), 83–84 .
    19. An analogue of the d’Alembert formula for the equations of a principal chiral field and the sine-Gordon equation.
      Dokl. Akad. Nauk SSSR 253:2 (1980), 288–292 .
    20. The inverse problem method and holomorphic bundles on Riemann surfaces.
      Soviet Sci. Rev. Sect. C: Math. Phys. Rev. 1 (1980), 5–26 (with S.P. Novikov).
    21. Methods of algebraic geometry in contemporary mathematical physics.
      Soviet Sci. Rev. Sect. C: Math. Phys. Rev. 1 (1980), 1–54 (with V.G. Drinfel’d, Yu.I. Manin, S.P. Novikov).
    1. On the rational solutions of the Zaharov-Šabat equations and completely integrable systems of N particles on the line. (PDF: Russian, English).
      Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 84 (1979), 117–130 .
    2. Rational solutions of duality equations for Yang-Mills fields. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 13:4 (1979), 81–82 .
    3. Holomorphic bundles and nonlinear equations. Finite-gap solutions of rank 2. (PDF: English)
      Dokl. Akad. Nauk SSSR 247:1 (1979), 33–37 (with S.P. Novikov).
    4. Holomorphic bundles and the Kadomcev-Petviašvili equation. (PDF: Russian)
      Uspehi Mat. Nauk 33:5(203) (1978), 209–211. (with S.P. Novikov)
    5. Algebraic curves and nonlinear difference equations. (PDF: Russian, English)
      Uspekhi Mat. Nauk 33:4(202) (1978), 215–216 .
    6. Holomorphic vector bundles over Riemann surfaces and the Kadomcev-Petviašvili equation. I. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 12:4 (1978), 41–52 (with S.P. Novikov).
    7. Commutative rings of ordinary linear differential operators. (PDF: Russian, English)
      Funktsional. Anal. i Prilozhen. 12:3 (1978), 20–31 .
    8. Rational solutions of the Kadomcev-Petviašvili equation. (PDF: Russian)
      Uspehi Mat. Nauk 33:2(200) (1978), 227–228 .
    9. Rational solutions of the Kadomcev-Petviašvili equation and the integrable systems of N particles on a line. (PDF: Russian, English)
      Funkcional. Anal. i Priložen. 12:1 (1978), 76–78 .
    10. Methods of algebraic geometry in the theory of nonlinear equations. (PDF: Russian,English)
      Uspehi Mat. Nauk 32:6(198) (1977), 183–208 .
    11. Geometry of Riemann surfaces and non-linear differential equations. (PDF: Russian)
      Uspehi Mat. Nauk 32:1(193) (1977), 229–230 (with B.A. Dubrovin).
    12. Integration of nonlinear equations by the methods of algebraic geometry. (PDF:Russian, English)
      Funkcional. Anal. i Priložen 11:1 (1977), 15–31 .
    13. Algebraic curves and commuting matrix differential operators. (PDF: Russian,English)
      Funkcional. Anal. i Priložen 10:2 (1976), 75–76 .
    14. The Schrödinger equation in a periodic field and Riemann surfaces. (PDF: English)
      Dokl. Akad. Nauk SSSR 229:1 (1976), 15–18 (with B.A. Dubrovin, S.P. Novikov).
    15. An algebraic-geometric construction of the Zaharov-Šabat equations and their periodic solutions.
      Dokl. Akad. Nauk SSSR 227:2 (1976), 291–294 .
    16. Obstructions to the existence of S1-actions. Bordisms of branched coverings.(PDF: Russian, English)
      Izv. Akad. Nauk SSSR Ser. Mat. 40:4 (1976), 828–844 .
    17. The potentials with zero reflection coefficient on the background of the finite-gap potentials. (PDF: Russian, English)
      Funkcional. Anal. i Priložen 9:2 (1975), 77–78 .
    18. Equivariant Hirzebruch genera. The Atiya-Hirzebruch formula. (PDF: Russian)
      Uspehi Mat. Nauk 30:1(181) (1975), 243–244.

6.  Formal groups and Atiyah-Hirzebruch formula. (PDF: Russian, English)
Izv. Akad. Nauk SSSR 38:6, (1974), 1289–1304.

5.  A remark on the paper “Actions of finite cyclic groups on quasicomplex manifolds” . (PDF: Russian, English)
Mat. Sb. (N.S.). 95(137):1(9) (1974), 146–147.

4. On invariance of the characteristic classes for the manifolds of the homotopy type of CP(n). (PDF: Russian)
Uspehi Mat. Nauk 28:5(173) (1973), 245–246.

3. Actions of finite cyclic groups on quasicomplex manifolds. (PDF: Russian, English)
Mat. Sb. (N.S.). 90(132):2 (1973), 306–319.

2. Formulae for the fixed points of an action of the group Zp. (PDF: Russian)
Uspehi Mat. Nauk 28:1(169) (1973), 237–238 (with S.M. Gusein-Zade).

1. Bordisms of groups acting freely on spheres. (PDF: Russian). Uspehi Mat. Nauk 26:6(162) (1971), 245–246.

antonzorich
Anton Zorich
Principal Research Scientist
romantravkin
Roman Travkin
Senior Research Scientist
charlesfougeron
Charles Fougeron
Research Scientist
igormakhlin
Igor Makhlin
Research Scientist

ФИО: Кричевер Игорь Моисеевич
Занимаемая должность (должности): Профессор, директор Центра Сколтеха по перспективным исследованиям
Преподаваемые дисциплины: –
Ученая степень: Кандидат физико-математических наук, МГУ (1975),  Д-р физико-математических наук (1984)
Ученое звание (при наличии): Профессор
Данные о повышении квалификации и/или профессиональной переподготовке (при наличии): нет
Общий стаж работы: более 40 лет
Стаж работы по специальности: более 40 лет