Novikov, Sergei Petrovich
Department
of geometry and topology (Head of the Department)
Office: 528
Phone: (095) 135 14 90
Email: snovikov@mi.ras.ru, novikov@ipst.umd.edu
Principal
fields of research:
Geometry and Topology (Algebraic, Homotopy and Differential Topology, Foliations, Topological Phenomena
in Variational Calculus).
Dynamical Systems.
Mathematical and Theoretical Physics (The Methods of Algebraic, Symplectic, Riemannian Geometry, Topology and
Dynamical Systems in General Relativity,
Completely Integrable Systems and Solitons, Magnetoresistence in Metals, Field Theory, Quantum Theory and Spectral Theory of Operators on Lattices and Graphs).'
Vita and
Education
Employment
Special
Service
Awards
and Honors
Selected
Honorable Invited Talks
The
Scientific School
Scientific
Results
Publications
(click this item to access the list of publications; for the highlighted items
in the list the full texts are available at this page)
Born:
Father - Petr Sergeevich Novikov (1901-1975),
outstanding mathematician (Descriptive Set Theory, Inverse Problem for the
Newtonian Gravity, Mathematical Logic and Combinatorial Group Theory),
Mother - Keldysh Lyudmila Vsevolodovna (1904-1976),
well-known mathematician, full professor (Set Theory and Geometric Topology).
1955-1960 Study in Moscow State University Department
of Mathematics and Mechanics,
1960 Student diploma from the Department of
Mathematics and Mechanics of MSU.
Thesis title: "Homotopy properties of Thom complexes", (Prof. M. M.
Postnikov -- adviser).
1960-1963 Aspirantura, the Steklov Institute of
Mathematics (Prof. M. M. Postnikov -- adviser).
1964 Candidate of Science (=PhD) in Physics and
Mathematics.
Thesis title: "Differentiable sphere bundles".
1965 Doctor of Science in Physics and Mathematics,
Thesis title: "Homotopy equivalent smooth manifolds".
1962 Married Eleonora Tsoi (Novikova), 3 children, 1 son (Petr) and 2 daughters(Irina and Maria).
1963-1975: The staff at the Steklov Institute of Mathematics,
junior researcher till 1965, senior researcher
after 1965
1965 - The staff at the Department Mathematics and Mechanics
of Moscow State University, Chair of Differential Geometry,
full professor since 1967
1971 - 1993 Head of the Mathematics Group at the L. D. Landau
Institute for Theoretical
Physics of the Academy of Sciences of the USSR,
after 1993--Principal Researcher in the same Institute
1983 - Head of the Chair in Higher Geometry and Topology
of Moscow State University
1984 - Head of the Group in Geometry and Topology of the Steklov
Mathematical Institute
of the Academy of Sciences of the USSR
02/1991-08/1991 Research professor, Laboratory of Theoretical
Physics, Ec. Norm. Sup. de Paris, France
1992-1996, Spring Semesters
University of Maryland at
College Park, visiting professor.
1996- full professor IPST
and Math Department, Distinguished Professor since 1997.
June 2000,
June 2001
and November 2002- Visiting Distinguished Professor of KIAS, (South)
Korean Republic, Seoul.
2009 - February 01 - March 30 and May 10 - June 10, Newtone Institute for Math
Sciences, Cambridge, UK: Invited Prticipant of the Program "Discrete Integrable Systems"
1983--1986 and
2000--2002 Member of Fields Medal Committees of The
International Mathematical Union
(for the International Mathematical Congresses in Berkeley, 1986
and Beigin, 2002)
1985--1996 President of the Moscow Mathematical Society
1986--1990 Vice--President of the International Association of Mathematical Physics
1986-- Editor-in-Chief of the Journal ''Uspekhi Math Nauk'' (=
''Russia Math Surveys'')
1967-1972 Member of Lenin Komsomol Prize Committee for young scientists;
Chairman of the Expert Group in Mathematics, Mechanics and Informatics.
1983-1988 Member of Expert Committee in Mathematics, Mechanics and Informatics
of the Highest Attestation Committee (VAK USSR)
1983-2007 Member of International Lobachevski Prize Committee of USSR/
Russian Academy of Sciences; Chairman after 1991.
1985-1991 Member of Expert Group in Mathematics, Mechanics and Informatics
of Lenin and State Prize Committee of USSR.
1983-2001 Member of Expert Group in Mathematics, Mechanics and Informatics
of State Prize Committee of Russian Federation.
1984--1991 Head of the Geometry/Topology Problem Committee
at the Mathematical Division of the Academy of Sciences of USSR
1994--1996 Member of the Program Committee of the European Math.
Society
(for the 2nd European Math Congress, Budapest, July 1996)
1995--1998 Member of the Program Committee of the International
Mathematical Union
(for the International Mathematical Congress, Berlin, August 1998).
1993--1998 Head of the Expert Committee in Mathematics, Mechanics, Informatics
in the Russian Foundation for the Fundamental Research (RFFR)
2001--2002 Co-chair (with P-L. Lions) of the International Program
Committee for the European Conference in Applied Mathematics/
Applications of Mathematics= AMAM2003
(Nice, 2003)
2006-2007 Member of the Shaw Prize Committee
2008- Member of the Abel Prize Committee
1964- Moscow Math Society Award for young mathematicians
1966-1981 Corresponding member of the
1967 - Lenin Prize
1970 - Fields Medal of the International Mathematical
Union
1981 - Lobachevskii International Prize of the
1981 - Full Member of the
1987 - Honorary Member of the London Math. Society
1988 - Honorary Member of the Serbian Academy of Art
and Sciences
1988 – Doctor Honoris Causa, University of Athens
1991 - Foreign Member, "Academia de Lincei",
Italy
1993- Academia Europea, member
1994 - Foreign associate, National Academy of
Sciences, USA
1996 - Member, Pontifical Academy of Sciences
(Vatican)
1997 - Distinguished University Professor, University
of Maryland at College Park
1998 - Conferences in Honor of 60th birthday:
Solitons, Geometry, Topology: On the Crossroads,
a)Steklov Math Institute and Landau Institute for
Theor Physics, Moscow, Russia, May 26-31, 1998
b)University of Maryland at College Park, College
Park, MD, September 24-26, 1998.
1999 - Doctor Honoris Causa,
2003 – Fellow,
2005 - Wolf Prize in Mathematics
2008 - Pogorelov Prize of the Ukranian National Academy of Sciences (NANU)
2009 - Bogoliubov Gold Medal of the Russian Academy of Sciences and Dubna Institute
for the Nuclear Research
Some Selected
Honorable Invited Talks:
1978 Plenary Speaker of the International Mathematical Congress, Helsinki
(Theory of Solitons and Algebraic Geometry)
1966 Invited Speaker of the International Mathematical
Congress, Moscow, Section of Topology (Presented to the Congress preprint of
the lecture ''Pontryagin Classes, the Fundamental Group and Some Problems of
the Stable Algebra'' - later published in the special edition dedicated to 70th
birthday of Georges de Rham; actually made talk in the Cobordism Theory)
1970 Invited Speaker of the International Mathematical
Congress, Nice, Section of Topology (''Hermitian Analog of the K-theory and
Hamiltonian Formalism''; has not been permitted to attend Congress personally
as a punishment for the letters supporting dissidents; the lecture has been
read by other person and published in the Materials of the Congress).
1977, 1981, 1986, 1988 Invited Plenary Speaker of the
International Congresses in Mathematical Physics in Rome, W.Berlin, Marceille
and Swansea
1992 Fermi Lectures, Scuola Normale Superior di Pisa,
''Solitons and Geometry'' (published by Cambridge University Press in 1994).
1994 Leonardo da Vinci Lecture, University of Milan,
''Algebraic Geometry and Solitons''
2000 Pollack Distinguished Lectures Series,
Haifa, Technion, Israel, ''2D Schrodinger Operators and Discrete Spectral
Symmetries'', ''Operators on Graphs and Symplectis Geometry'',
''Topological Phenomena in Normal Metals''
Over 30 Novikov's students became PhD. Part of them got the scientific degree
''Doctor of Physico-Mathematical Sciences'' (the second doctor degree
equivalent to the scientific level of full professor):
V.Golo, V.Buchstaber**, A.Mishchenko**, G.Kasparov**,
O.Bogoyavlenski**, F.Bogomolov**, S.Gusein-Sade, I.Krichever**,**,
B.Dubrovin**,**, I.Taimanov, A.Veselov*, I.Babenko, R.Nadiradze, V.Vedenyapin, M.Brodski,
S.Tsarev, O.Mokhov, R.Novikov, P.Grinevich, I.Dynnikov*, A.Maltsev.
Other former students of S. Novikov who received the
PhD level or the scientific degree ''Candidate of Physico-Mathematical
Sciences'' (which is a Soviet/Russian equivalent of PhD) are the following:
A.Brakhman, V.Peresetski, A.Grigoryan, Th.Voronov,
A.Zorich, N.Panov, A.Lyskova, M.Pavlov, Le Tu Thang, L.Alania, D.Millionshikov,
S.Piounikhin, V.Sadov, A.Lazarev, R.Deleo, A.Giacobbe, K.Kaipa.
People whose names are marked by ** were invited
speakers of the International Math Congresses or the plenary speakers of the
European Math Congresses and/or International Congresses in Math Physics, the
names marked by * were invited section speakers of the European Math
Congresses.
Topology
Differentiable Manifolds and Characteristic Classes
Topological Invariance of Rational Pontryagin Classes
(1965).
Homotopy Invariance of the special
Pontryagin-Hirzebruch Integrals along the cycles coming from the Homological
Algebra of fundamental group (1965-70). The Higher Signature Conjecture -
''Novikov Conjecture'' (1970). Hermitian Analog of the Algebraic K-Theory for
the rings with involution and Symplectic Algebra (1970).
Classification of the closed simply connected
manifolds (n>4 ) of the same tangential homotopy type.
Browder-Novikov theory. There is only a finite number of manifolds with the
same Rational Pontryagin Classes (1961-64).
The Recognition Problem of the n-sphere is
undecidable for n>4 (1962, published later): it was included in the article of I.Volodin,
V.Kuznetsov and A.Fomenko as $ 10. A theorem of S.P.Novikov
Study of Multiplicative Structure in the Rings of Stable Homotopy Groups of Spheres
and Cobordisms
First proof of existence of arbitrary long nontrivial superpositions in the Stable Homotopy Ring
for Spheres (1959):calculation of multiplication in the most important old and new cobordismrings:
Real Orientable and Unitary --- see footnote to the item n 6 of publications about the priority
relations here; Special Unitary and Symplectic. These results are based on the developement of
algebraic and geometric technique associated with Adams
Spectral Sequence. In particular, cohomology of Hopf Coalgebras and new type ''Steenrod-like''
Operations in cohomology of Hopf
Algebras over the finite fields play fundamental role here(1959-62).
New Methods of Algebraic Topology from the viewpoint of
Complex Cobordism Theory, the Adams-Novikov Spectral Sequence. Complete calculation of
the ''Steenrod'' algebra of operations as the Operator
(Heisenberg) double over the Landveber-Novikov Hopf algebra with specific
Z-structure (see the items nn 122, 152 for the latest development of algebraic aspects).
Application for the study of the stable homotopy groups of spheres. Discovery of Formal
Groups of ''Geometric Cobordisms'' (Novikov-Mischenko, 1967) and its applications: the ''Adams-type''
operations in complex cobordisms; the analog of Chern Character;
Cyclic Group actions and Fixpoint Equations, calculation of the Hirzebruch
Multiplicative Series through the Formal Group (1966-1971). Further development of algebraic structures
associated with unitary cobordisms, the fixpoint equations, 2-valued formal group (Buchstaber-Novikov, 1971)
Nonsingular Foliations
Qualitative Theory of The Nonsingular Codimension One
Foliations, especially on 3-manifolds. Existence of Compact Leave
for any nonsingular 2-foliation on 3-sphere and many other 3-manifolds,
classification of all topological types of
analytical foliations in the solid torus based on the conjugacy classes of braids
(1963-65). Resent results: Topology of the
generic foliations on Riemann Surfaces generated by the real parts
of holomorphic one-forms. Transversal Canonical Bases and
Fundamental Semigroup of positive closed transversal curves, its
calculation based on the Continued Fractions (2004-2005)
Morse-Type Theory
Morse-Type Theory for the closed 1-forms on manifolds
(The Morse-Novikov Theory). Novikov Inequalities for the numbers of critical points
(1981). Topology of foliations generated by the closed one-form with Morse
singularities. The Quasiperiodic manifolds. Novikov Conjectures concerning the
structure of leaves and analytical properties of the Morse-Novikov Complex
generated by the closed 1-form and C1-generic Riemannian metric (1981-1991).
Morse Theory for the non-simply-connected manifolds.
Morse inequalities and representations of fundamental group, the jumping
subvarieties for homology groups on the representation space (the analogs of
Alexander Polinomials). Complete calculation of the generic Betti number and all Milnor-Farber
Spectral Sequence for one-dimensional representations through the Massey
Operations (1986). Von Neumann factors and Morse inequalities, the Novikov-Shubin
invariants of the Laplace-Beltrami Operators on universal covering. The Von Neumann
analog of the Reidemeister-Ray-Singer Torsion. Analog of Morse-Witten
inequalitis for smooth real vector fields and diagonalization of real fermionic
quadratic forms (1986-87). Recent results: The Exotic De Rham cohomology,differential
forms and dynamical systems: new functors and exact sequences (Novikov, 2007-2008).
Closed one-forms in the Variational Calculus (Multivalued Action
Functionals on the spaces of mappings).
Classification of the ''local'' 1-forms in the field theory
(1981-82). Nonlocal 1-forms on the spaces of
mappings of spheres in the manifolds, the Analytical
Homotopy Theory, Module Spaces in The Rational (Real) Homotopy Theory (1984-88).
Topology and Qualitative Dynamics in Physics
General Relativity (1972-75):
Spacely Homogeneous Solutions for the Einstein
Equation with Hydrodynamic Energy-Momentum Tensor (Homogeneous Cosmological
Models). Full description of the nondegenerate compactification of Phase Space and
System near Cosmological Singularity. Properties of the ''Typical'' Evolution and
their dependence on the
sign of time: the mixmaster (BLKh) regime survives as a typical with
probability one for the Collapsing Universe only; it disappears for the
Expansion Process immediately; some specific set of the power-like regimes are
typical for the Expanding Universe. Strict Isotropization of the Early Universe
does not follow from the classical Einstein Equation with normal physical
energy-momentum tensor (positive energy and pressure): only weak
isotropization in the first approximation of the Hubble constants in different
directions follows from dynamics. However, the real Universe has been strictly
isotropic on the large scale as it became finally clear after the later
observations of the background radiation in the late 80s.
2D Schroedinger Operators in Topologically Nontrivial Magnetic Fields and
Lattice:
Periodic Schroedinger Operator as the family of Hermitian
Operators with Discrete Finite Multiplicity Spectrum, the notion of Generic
Families of the hermitian Matrices and Chern Classes of the Dispersion Relations, their role
in Quantum Physics (1980-83).
Analytical Mechanics and Applications of Symplectic Geometry:
Factorization of the Top (Solid Body) moving in the ideal incompressible fluid
by the Hamiltonian circle action is isomorphic
to the Dirak Monopole on the 2-sphere with some Riemannian metric, other
physical systems of that type in the Classical Mechanics and Modern Physics; Magnetic Field as a correction
of the factorized Symplectic Structure (1981). Morse type theory for the
charged particle in the magnetic field and ''Other-throwing of the Cycles''
Principle (1981-1984, 1994, Novikov-Taimanov-Grinevich).
Quantum Field Theory - Topological Phenomena:
Multivalued Action Functionals in Mathematical and
Theoretical Physics, Classification of the local closed one-forms on the spaces
of mappings: Topological Quantization of Coupling Constants as a Corollary from
the Requirement that the Feinmann Amplitude should be one-valued (i.e.
circle-valued) map, Wess-Zumino-Novikov-Witten Model (1981-82).
Real Physics:
Topological Phenomena in Normal Metals, especially
in the noble metals. Classification of generic Electrical Conductivity Tensors in the
Strong Magnetic Fields for the normal metals with topologically complicated Fermi Surfaces.
New observable integer-valued quantities. Topology of the Quasiperiodic Functions
on the Plane and its applications (2002-2004), Novikov-Dynnikov-Maltsev.
Right definition of the symmetry group for Quasi-Crystals (the
Quasi-Crystallographic Groups) was invented in 1986. Nontrivial examples for the 2D case were found with infinite rotational part= factor-group by translations (S.Novikov-A.Veselov).
This approach is different from all other authors who assumed that the rotational part is finite. This result was published later (it was included in the article of Le Thang, S.Piunikhin, V.Sadov published in the Russian Mathematical Surveys
(1993), vol. 48 n1, pp 37-100, where symmetry theory for Quasi-Cristals was developed by Piunikhin).
Exactly Solvable Linear and Nonlinear Systems
Methods of Algebraic Geometry
Finite-Gap Periodic and Quasiperiodic KdV Solutions:
Discovery of finite-gap (algebrogeometric) Periodic and Quasiperiodic 1D
Schroedinger Operators and finite-Gap (algebrogeometric) solutions to KdV
equation, lambda-polinomial Zero-Curvature Representation for all higher
KdV systems and corresponding Lax representation for the Stationary Equations,
Hyperelliptic Riemann surfaces and Finite-Gap Property (1974); Analysis on the
Riemann Surfaces and Abelian Varieties, q-functions, Hamiltonian
Integrability of the Stationary Systems. The whole Family of Hyperelliptic Jacobian
Varieties is Unirational with specific effectively written polinomial formulas
in the space Cn. The complete solution of the inverse finite-gap
periodic problem (Dubrovin-Novikov, 1974-76). The ''Novikov Conjecture'' for the Solution of the
Riemann-Shottki Problem as a by-product of the Soliton Theory (Novikov-Dubrovin, 1979).
2D periodic Schroedinger Operators:
Operators with one selected level such that the
Fermi-Curve is algebraic, 2+1 Nonlinear Systems as deformations of the
Schroedinger Operators with selected spectral level (the Manakov's L-A-B-triples) and algebrogeometrical
solutions (1976). Solution of Inverse Spectral Problem for the purely potential
periodic operators with algebraic Fermi-Curve, Prym q-functions, Novikov-Veselov equation and Hierarchy (1984-86). The Big
Norm Problem for rapidly decreasing 2D operators, its solution for the "levels below the ground state" based on
the Generalized Analytical Functions (Grinevich-Novikov, 1989).
Higher Rank Problems:
Families of Higher rank Commuting Linear OD Operators and KP Hierarchy.
Framed Holomorphic vector bundles over Riemann Surfaces, KP Hierarchy and
Method of deformation of the Tyurin Parameters. Complete solution for the case
of Elliptic Curve rank 2. Krichever-Novikov Equation (1978-80). Commuting
Higher rank linear OD operators with periodic Coefficients: Novikov Principle
on the comparison of the Bloch and Burchnall-Chaundy Riemann Surfaces. The
Spectral Theory of rank l operators of order N=lk as theory of
order k operators with spectral parameter on Riemann Surface, the case k=2,
l=2 (1981-1982). The difference higher rank commuting operators
(Krichever-Novikov, 1999, 2005).
Algebraic Geometry and Action-Angle Variables:
Specific Poisson Structures associated with Completely Integrable
Systems based on Riemann Surfaces. First Calculation of Action-Angle
variables for the classical Kovalevskaya Top and other systems
(Novikov-Veselov,1881-84).
The special features of the real finite-gap solutions of
Sine-Gordon System}: The very fact that main problems of this theory
are unsolved, is revealed. New ideas are proposed how to calculate
the Topological Charge through the inverse spectral data
(Dubrovin-Novikov, 1982-1984). Complete Solution of the
Topological Charge Problem, its calculation in terms of the inverse
spectral (algebro-geometrical) data (Grinevich-Novikov, 2001-2002).
Riemannian Geometry and Hydrodynamic Type Systems, Nonlinear WKB-Type
asymptotics for KdV:
Hamiltonian Hydrodynamic Type Systems and Hydrodynamic
Type Poisson Structures (Dubrovin-Novikov brackets). Nonlinear WKB (Whitham
Method) and Hamiltonian Hydrodynamic Type Systems (1983-85) Linear brackets and
special Virasoro-Type Lie Algebras of vector-functions, Frobenius algebras and
Riemannian Geometry (1985). Evolution of Multivalued Functions in the Witham Metod for KdV, numerical
studies and formulation of boundary conditions, the influence of viscosity
(Avilov, Novikov, Krichever, 1986-88). Recent results: The theory of Weakly Nonlocal Poisson Structures (Maltsev-Novikov,
2000-2002)
Fourier Series and Riemann Surfaces. Quantum Bosonic Strings:
The Operator Construction of the Multiloop Interacting
Bosonic Quantum String Theory, Analogs of the Fourier Series on the Riemann
Surfaces. Krichever-Novikov bases and algebra's, the almost graded multiplication property
(1987-90). Recent results: The continious analogs of Fourier bases on Riemann Surfaces, Indefnite Hilbert Spaces and finite-gap operators with singularities
(Grinevich-Novikov, 2003, 2008-2009)
String Equation:
Theory of the ''String Equation from the Matrix
Models'' [L,A]=1 (in particular, of the Painleve'-I equation), Soliton
Theory, different Asymptotic Methods, the Special Semiclassics for the Lax Pair
associated with the Physical Solution. The String Equation as an algebraic object: the
Painleve'-I equation can be presented as an equation on the module space of the elliptic curves
(1990-1995)
2D Nonrelativistic Pauli Operator for the electron moving in the arbitrary Periodic Magnetic Field, the infinitely high
degeneracy and complete solvability of the ground level (Dubrovin-Novikov, 1980). Cyclic, Semicyclic and Quasicyclic
Laplace Chains for the 2D Schroedinger operators in periodic magnetic field and potential, the operators with pair of infinitely degenerate exactly solvable energy levels (Novikov-Veselov, 1995-97).
Discrete analogs of the Laplace transformations: the Elliptic and Hyperbolic cases, Exactly solvable operators (1996-1997).
Discretization of Differential-geometrical Connection on the Triangulated Manifolds and linear difference triangle operators. New discretization of
Complex Analysis for the Euclidian plane (Novikov-Dynnikov, 1997, 2001-2004) and Hyperbolic (Lobachevski) Plane (Novikov, 2008).
:
Graphs and Symplectic Geometry:
Scientific Works, Survey Articles, Textbooks
1. Cohomology of the Steenrod algebra.
Dokl. Akad. Nauk SSSR, 1959, v. 128, N 5, 893-895 (submitted 29.05.1959).
Linear Sef-Adjoint Systems on Graphs, Discovery of Symplectic
Wronskians and their Symplecto-Topological Properties. Scattering
Theory and Symplectic Geometry: The Scattering Matrix is always
Symmetric Unitary Matric for real operators on graphs with tails
(1997-1999)}. Symplectic Wronskian for Nonlinear Systems
(Novikov-Schwarz, 1999).
Integrable Soliton Systems on the trivalent tree, fourth order
selfadjoint operators and Laplace Transformations.
(Krichever-Novikov, 1999-2000).
and
Popular Articles in Mathematics and Math Physics [2]
2. Some problems in the topology of manifolds connected with the theory of Thom
spaces. Dokl. Akad. Nauk SSSR, 1960, v. 132, N 5, 1031-1034 (submitted 16.02.1960).
3. On embedding simply-connected manifolds in Euclidean space. Dokl. Akad. Nauk
SSSR, 1961, v. 138, N 4, 775-778 (submitted 20.01.1961).
4. On the diffeomorphisms of simply-connected manifolds. Dokl. Akad. Nauk SSSR,
April 1962, v. 143, N 5, 1046-1049 (submitted 09.11.1961).
5. Smooth manifolds of a general homotopy type, Intern. Cong. Math.,
6. Homotopy properties of Thom complexes. Mat. Sb. 1962, v. 57, N 4,
406-442. English translation with the author’s comments.
7. Homotopy properties of the group of diffeomorphisms of a sphere. Dokl.
Akad. Nauk SSSR, 1963, v. 148, N 1, 32-35 (submitted 23.06.1962).
8. Some properties of (4k+2)-dimensional manifolds. Dokl. Akad. Nauk
SSSR, 1963, v. 153, N 5, 1005-1008 (submitted 13.06.1963).
9. Differential topology, Itogi Nauki (Algebra and Topology), Inst. Nauchn.
Informatsii Akad. Nauk SSSR, 1963, 134-160.
10. Homotopically equivalent smooth manifolds, I. Izv.
Akad. Nauk SSSR, 1964, v 28, N 2, 365-474.
11. Foliations of codimension 1 on manifolds, Dokl. Akad. Nauk SSSR, 1964, v.
155, N 5, 1010-1013.
12. Foliations of codimension 1, Dokl. Akad. Nauk SSSR, 1964, v. 157, N 4,
788-790.
13. Smooth foliations on three-dimensional manifolds, Uspekhi Mat. Nauk, 1964,
v. 19, N 6, 89-91.
14.
15. Gorki mathematical seminar on homotopic topology (June 1964), Uspekhi Mat.
Nauk, 1964, v. 19, N 6, 237-238 (with M. I. Vishik and M. M. Postnikov).
16. The Topology Summer Institute, Seattle, 1963, Uspekhi Mat. Nauk, 1965, v.
20, N 1, 147-170.
17. New ideas in algebraic topology (K-theory and its applications). Uspekhi
Mat. Nauk, 1965, v. 20, N 3, 41-66.
18. Homotopic and topological invariance of certain rational classes of
Pontryagin, Dokl. Akad. Nauk SSSR, 1965, v. 162, N 6, 1248-1251.
19. Topological invariance of rational Pontryagin classes, Dokl. Akad. Nauk
SSSR, 1965, v. 163, N2, 298-300.
20. Differentiable sphere bundles, Izv. Akad. Nauk SSSR,
1965, v. 29, N 1, 71-96.
21. Rational Pontryagin classes, Homeomorphism and homotopy
type of closed
22. Structures on manifolds, Proc. 4th All-Union Topology Conference (
23. The topology of foliations, Trudy Moskov. Mat. Obshch,
1965, v. 14, 248-278.
24. On manifolds with free Abelian fundamental group and their application,
Izv. Akad. Nauk SSSR, 1966, v. 30, N 1, 207-246.
25. Traces of elliptic operators on submanifolds and K-theory, Dokl. Akad. Nauk
SSSR, 1966, v. 170, N 6, 1265-1268 (with B. Yu. Sternin).
26. Elliptic operators and submanifolds, Dokl. Akad. Nauk SSSR, 1966, v. 171, N
3, 525- 528 (with B. Yu. Sternin).
27. The Cartan-Serre theorem and intrinsic homology. Uspekhi Mat. Nauk, 1966,
v. 21, N 5, 217-232.
28. Pontryagin classes, the fundamental group and some problems of stable
algebra. Int. Mat. Congr., Moscow, Thesis, 1966, 158-159 (preprint).
29. Second topology summer school (Druskininkai, Lithuanian SSR, 17-29 June
1965), Uspekhi Mat. Nauk, 1966, v. 21, N 2, 257-258 (with A. A. Kirillow, D. B.
Fuks and
30. Operation rings and spectral sequences of Adams type
in extraordinary cohomology theories, U-cobordisms and K-theory, Dokl. Akad.
Nauk SSSR, 1967, v. 172, N 1, 33-36.
31. Methods of algebraic topology from the point of view of cobordism theory.
Izv. Akad. Nauk SSSR, 1967, v. 31, N 4, 885-951.
32. Adams operators and fixed points. Izv. Akad. Nauk
SSSR, 1968, v. 32, N 6, 1245-1263.
33. Homotopic and differential topology history of mathematics in the
Fatherland, Naukova Dumka,
34. Pontryagin classes, the fundamental group and some problems of stable
algebra, in Essays on Topology and Related Topics. (Memoires dedies a Georges
de Rham), Springer,
35. Algebraic construction and properties of Hermitian analogues of K-theory
over ring with involution from the viewpoint of Hamiltonian formalism.
Applications to differential topology and the theory of characteristic classes,
I. Izv. Akad. Nauk SSSR, 1970, v. 34, N2, 253-288.
36. Algebraic construction and properties of Hermitian analogues of K-theory
over rings with involution from the viewpoint of Hamiltonian formalism.
Applications to differential topology and the theory of characteristic classes,
II. Izv. Akad. Nauk SSSR, 1970, v. 34, N 3, 475-500.
37. Analogues hermitiens de la K-theorie, Actes Congr. Intern. Math (Nice
1970), Gauthier-Villars,
38. Formal groups, power systems, and Adams operators.
Mat. Sb. 1971, v. 84, N 1, 81- 118 (with V. M. Buchstaber).
39. Formal groups and their role in the apparatus of algebraic
topology, Uspekhi Mat. Nauk, 1971, v. 26, N 2, 131-154 (with V. M.
Buchstaber and A. S. Mishchenko).
40. On some characteristics of cosmological models, Zh. Eksper. Teoret. Fiz.,
1972, v. 62, N 6, 1977-1990.
41. A necessary reconstruction of mathematical education, Priroda, 1973, N 2,
57.
42. Singularities of the cosmological model of the Bianchi IX type according to
the qualitative theory of differential equations, Zh. Eksper. Teoret. Fiz.,
1973, v. 64, N 5, 1475-1494 (with O. I. Bogoyavlenskii).
43. A periodic problem for the Korteweg-de Vries equations, I. Funktsional
Anal. i Prilozhen., 1974, v. 8, N 3, 54-66.
44. Periodic and conditionally periodic analogues of the many soliton solutions
of the Korteweg-de Vries equations, Zh. Eksper. Teoret. Fiz., 1974, v. 67, N
12, 2131-2143 (with B. A. Dubrovin).
45. A periodic problem for the Korteweg-de Vries and Sturm-Liouville equations.
Their connection with algebraic geometry, Dokl. Akad. Nauk SSSR, 1974, v. 219,
N 3, 531- 534 (with B. A. Dubrovin).
46. Qualitative theory of homogeneous cosmological models, Trudy Sem.
Petrovsk., 1975, v. 1, 7-43 (with O. I. Bogoyavlenskii).
47. The connection between the Hamiltonian formalisms of stationary and
nonstationary problems, Functional Anal. Appl., 1976, v. 10, N 1, 9-13 (with O.
I. Bogoyavlenskii).
48. Non-linear equations of Korteweg-de
Vries type, finite zone linear operators, and Abelian varieties,
Uspekhi Mat. Nauk, 1976, v. 31, N 1, 55-136 (with B. A. Dubrovin and V. B. Matveev).
49. The Schroedinger equation in a periodic field and Riemann surfaces, Dokl.
Akad. Nauk SSSR, 1976, v. 229, N 1, 15-18 (with B. A. Dubrovin and
50. Homogeneous models in general relativity theory
and gas dynamics ,
Uspekhi Mat. Nauk, 1976, v. 31, N 5, 33-48 (with. O.I. Bogoyavlenskii).
51. Algebraic topology, Encyclopedia of Mathematics, 1977, vol. 1, 170-174.
52. Petr Konstantinovich Rashevskii (on his seventieth Birthday), Uspekhi Mat.
Nauk, 1977, v. 32, N 5, 205-209 (with A. T. Fomenko).
53. Methods of algebraic geometry in contemporary mathematical physics, Math.
Phys. Reviews,1978, 1-54 (with V. G. Drinfel'd, I. M. Krichever and Yu. I.
Manin).
54. Problems in geometry,
55. Holomorphic vector bundles over Riemann surfaces and the
Kadomtsev-Petviashvili (KP) equation. I, Funktsional Anal. i Prilozhen, 1978,
v. 12, N 4, 41-52 (with. I. M. Krichever).
56. A method of solving the periodic problem for the Korteweg-de Vries equation
and a generalization of it, Proc. All-Union Conf. on partial differential
equations, dedicated to I. G. Petrovskii on his seventy-fifth birthday,
57. Algebraic geometry and mathematical physics, Proc. Conf. on fundamental
problems in mathematics and theoretical physics, dedicated to the 70th birthday
of Academician N. N. Bogolyubov, Joint Institute of Nuclear Research, Dubna,
1979, 459-473.
58. Modern geometry. Methods and applications, Nauka,
59. Holomorphic fiberings and non-linear equations. Finite zone solutions of
rank 2, Dokl. Akad. Nauk SSSR, 1979, v. 247, N 1, 33-37 (with
60. Solutions to the Ginzburg-Landau equations for planar textures in
superfluid He-3, Comm. Math. Phys., 1979, v. 69, 237-246 (with V. L. Golo and
M. I. Monastyrskii).
61. Methods of qualitative theory of dynamics systems in general relativity
theory, Non-linear waves, Nauka,
62. Holomorphic bundles over algebraic
curves and nonlinear equations. Uspekhi Mat. Nauk, 1980, v. 35, N 6, 47-68 (with
I.M. Krichever).
63. The theory of solitons and method of the inverse problem, Nauka,
64. Ground states of a two-dimensional electron in a periodic magnetic
field. Zh. Eksper. Teoret. Fiz., 1980, v. 79, N 3, 1006-1016 (with B. A.
Dubrovin).
65. Ground states in a periodic field. Magnetic Bloch functions and vector
bundles. Dokl. Akad. Nauk SSSR, 1980, v. 253, N 6, 1293-1297 (with B. A.
Dubrovin).
66. A method of solving the periodic problem for the KdV equations and its
generalization, in Solitons, ed R. K. Bullough and P. J. Caudrey, Topics in
Current Physics 17, Springer, Berlin - New York, 1980, 325-338.
67. Linear operators and integrable Hamiltonian systems, Proc. Intern. Congr.
Math. (Helsinki 1978), Helsinki, 1980.
68. Multivalued functions and functionals. An analogue of the Morse theory,
Dokl. Akad. Nauk SSSR, 1981, v. 260, N 1, 31-35.
69. Periodic solutions of the Kirchhoff equations for the free motion of a
rigid body in a fluid and the extended Lyusternik-Shnirel'man-Morse theory. I,
Funktsional Anal. i Prilozhen., 1981, v. 15, N 3, 54-66 (with I.Shmel'tser).
70. Variational methods and periodic solutions of equations of Kirchhoff type.
II, Funktsional Anal. i Prilozhen., 1981, v. 15, N 4, 37-52.
71. Bloch functions in a magnetic field and vector bundles. Typical dispersion
relations and their quantum numbers, Dokl. Akad. Nauk SSSR, 1981, v. 257, N 3,
538-543.
72. Kirchhoff type equations and many-valued functions and functionals.
Analogue of the Morse-Lyusternik-Shnirel'man theory and periodic orbits in a
magnetic field, Report to the I. G. Petrovskii seminar, Uspekhi Mat. Nauk,
1981, v. 36, N 5, 217-219.
73. Algebraic geometry and mathematical physics, in Proc. USA-USSR Conf. ed. V.
E. Zakharov and S. V. Manakov, North-Holland, Amsterdam 1981 (with I. M.
Krichever).
74. The Hamiltonian formalism and a
many-valued analogue of Morse theory, Uspekhi Mat. Nauk , 1982, v. 37, N 5, 3-49.
75. On Poisson brackets compatible with algebraic geometry and the Korteweg-de
Vries dynamics on the set of finite-zone potentials, Dokl. Akad. Nauk SSSR,
1982, v. 266, N 3, 533-537 (with A. P. Veselov).
76. Algebro-geometric Poisson brackets for real finite-zone solutions of the
sine-Gordon equation and the non-linear Schroedinger equations, Dokl. Akad.
Nauk SSSR, 1982, v. 267, N 6, 1295-1300 (with B. A. Dubrovin).
77. Commuting operators of rank l>1 with periodic coefficients, Dokl.
Akad. Nauk SSSR, 1982, v. 263, N 6, 1311-1314.
78. On the spectral theory of commuting operators of rank 2 with periodic
coefficients, Funktsional Anal. i Prilozhen., 1982, v. 16, N 1, 25-26 (with P.
G. Grinevich).
79. Topological and algebraic-geometrical methods in contemporary mathematical
physics, Soviet Scientific Reviews, 1982, v. 3, 1-156 (with B. A. Dubrovin and
I. M. Krichever).
80. Hamiltonian formalism of one-dimensional systems of hydrodynamic type and
the Bogolyubov-Whitham averaging method, Dokl. Akad. Nauk SSSR, 1983, v. 270, N
4, 781-785 (with B. A. Dubrovin).
81. Two-dimensional Schroedinger operators in periodic fields. Current Problem
in Mathematics, VINITI, 1983, v. 23, 3-22.
82. Multivalued functionals in modern mathematical physics, Atti Accad. Sci.
Torino Cl. Sci. Fis. Mat. Natur, 1983, v. 117, suppl. 2, 635-644.
83. The analytic generalized Hopf invariant.
Many-valued functionals, Uspekhi Mat. Nauk, 1984, v. 39, N 5, 97-106.
84. Critical points and level surfaces of many-valued functions, Trudy Mat.
Inst. Steklov, 1984, v. 166, 201-209.
85. Poisson brackets and complex tori. Trudy Mat. Inst. Steklov, 1984, v. 165,
49-61 (with A.P.Veselov).
86. Modern geometry. Methods of homology theory, Nauka, Moscow 1984 (with B. A.
Dubrovin and A. T. Fomenko).
87. Periodic extremals of many-valued or not everywhere positive functionals,
Dokl. Akad. Nauk SSSR, 1984, v. 274, N 1, 26-28 (with I. A. Taimanov).
88. On Poisson brackets of hydrodynamic type, Dokl. Akad. Nauk SSSR, 1984, v.
279, N 2, 294-297 (with B. A. Dubrovin).
89. Discussion with Academician S. P. Novikov, Kvant, 1984, N 10, 2-5.
90. Finite-zone two-dimensional potential Schroedinger operators. Explicit
formulas and evolution equations, Dokl. Akad. Nauk SSSR, 1984, v. 279, N 1,
20-24 (with A. P. Veselov).
91. Finite-zone two-dimensional Schroedinger operators. Potential operators,
Dokl. Akad. Nauk SSSR, 1984, v. 279, N 4, 784-788 (with A. P. Veselov).
92. Algebro-topological approach to reality problems Real action variables in
the theory of finite-gap solutions of the sine-Gordon equation. Zap. Nauchn.
Sem. LOMI, 1984, v. 133, 177-196
93. An averaging method for one-dimensional systems, in Non-linear and
Turbulent Process in Physics, vol 3, Harwood Academic Publ. Chur. 1984,
1529-1540.
94. The geometry of conservative systems of
hydrodynamic type. The method of averaging for field-theoretical systems.
Uspekhi Mat. Nauk, 1985, v. 40, N 4, 78-89.
95. Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras,
Dokl. Akad. Nauk SSSR, 1985, v. 283, N 5, 1036-1039 (with A. A. Balinskii).
96. Algebraic topology at the Steklov Mathematical Institute of the Academy of
Sciences of the USSR, Trudy Mat. Inst., Steklov, 1985, v. 169, 27-49.
97. Analytical homotopy theory. Rigidity of homotopic integrals, Dokl. Akad.
Nauk SSSR, 1985, v. 283, N 5, 1088-1091.
98. Integrable systems, I. Current problem in mathematics. Fundamental
directions. VINITI, 1985, v. 4, 179-284 (with B. A. Dubrovin and
99. Two-dimensional periodic Schroedinger operators and Prym's q-functions, in Geometry Today, Internat. Conf. Rome, June 1984,
100. Differential geometry and the averaging method for field-theoretic
systems, Proc. III Internat. Symp. on Selected Problem in Statistical Mechanics
(Dubna, 1984), Joint. Institute of Nuclear Research, Dubna, 1985, vol. 2,
106-118.
101. Modern geometry. Methods and applications. 2nd revised edition, Nauka,
102. Bloch homology. Critical points of functions and closed I-forms, Dokl.
Akad. Nauk SSSR, 1986, v. 287, N 6, 1321-1324.
103. Morse inequalities and von Neumann 1-factors, Dokl. Akad. Nauk SSSR, 1986,
v. 289, N 2, 289-292 (with M.Shubin).
104. Topology I. Current problem in mathematics. Fundamental directions,
VINITI, 1986, v. 12, 5-251.
105. Two-dimensional Schroedinger operators: Inverse
scattering transform and evolutional equations, Phys. D18, 1986, 267-273
(with A. P. Veselov).
106. Vladimir Abramovich Rokhlin (obituary), Uspekhi Mat. Nauk, 1986, v. 41, N
3, 159-163 (with V. I. Arnol'd, D. B. Fuks, A. N. Kolmogorov, Ya. G. Sinai, A.
M. Vershik, and O. Ya. Viro).
107. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad.
Nauk SSSR, 1987, v. 294, N 2, 325-329 (with V. V. Avilov).
108. Elements of differential geometry and topology, Nauk,
109. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad.
Nauk SSSR, 1987, v. 295, N 2, 345-349 (with V. V. Avilov and
110. Algebras of Virasoro type, Riemann surfaces and
structures of the theory of solitons, Funktsional. Anal. i Prilozhen.,
1987, v. 21, N 2, 46-63 (with
111. Virasoro-type algebras, Riemann surfaces and strings in
Minkowski space, Funktsional. Anal. i Prilozhen., 1987, v. 21, N 4, 47-61
(with
112. Two-dimensional Schroedinger operator and solitons: 3-dimensional
integrable systems. VIII Internat. Congr. on Math. Physics, Marseille 1986,
World Scientific Publ. 1987, 226-241.
113. The two-dimensional inverse scattering problem for negative
energy and generalized analytic functions, I. Energy below the basis state,
Funktsional. Anal. i Prilozhen., 1988, v. 22, N 1, 23-33 (with P. G.
Grinevich).
114. Analytical theory of homotopy groups, in Topology and Geometry, Rochlin
Seminar, Lecture Notes in Math., 1988, vol. 1346, 99-112, Springer-Verlag.
115. Algebras of Virasoro type, energy-momentum tensor and
decomposition operators on Riemann surfaces, Funktsional. Anal. i
Prilozhen. 1989, v. 23, N 1, 24-40 (with
116. Hydrodynamics of the soliton lattices. Differential
geometry and Hamiltonian formalism. Uspekhi Mat. Nauk, 1989, v.44, N 6,
29-98 (with B. A. Dubrovin).
117. Riemann surfaces, operator fields, strings. Analogues of the
Fourier-Laurent bases, in Memorial Volume for Vadim Knizhnik, "Physics and
Mathematics of Strings", eds. L. Brink, D. Friedan, A. M. Polyakov, World
Scientific,
118. On the quantization of finite-zoned potentials in connection with string
theory, Funktsional. Anal. i Prilozhen., 1990, v.24, N 4, pp 43-53.
119. On the equation [L,A] =\eps{\cdot}1, Progress of Theor Physics,
Suppliment n 102, 1990, Kyoto, Japan, pp 287-292
120. Riemann Surfaces, Operator Fields, Strings. Analogues of the
Fourrier-Laurent bases. Progress of Theor Physics, Suppliment n 102, 1990,
121. Hydrodynamics of the Soliton Lattices and Differential Geometry.
(Collection of the survey articles.
122. Various doubles of the Hopf algebras. Operator algebras on the quantum
groups and Complex Cobordisms, Uspekhi Math. Mauk, 1992, v. 47 iss. 5, pp.
189-190, arXiv,
math-ph/0004016.
123. Action-angle Variables and Algebraic Geometry, in the volume La
''Mechanique Analitique'' de Lagrange et son heritage-II, Accademia delle
Scienze di Torino Suppl, 1992, v126, n 2, pp 139- 150.
124. Integrability in Mathematics and Theoretical Physics: Solitons. The
Mathematical Intelligencer, 1992, Vol. 14, N 4.
125. Role of Integrable Models in the development of Mathematics. (Mathematical
Research today and tomorrow: Viewpoints of seven Fields Medallists). LNM,
1992, v 1525, Springer
126. Quasiperiodic structures in Topology, In: Topological Methods in
Modern Mathematics (Dedicated to the 60th birthday of J. Milnor.
Stony=Brook University, 1991).
127. On the Liouville form of the Poisson bracket of Hydrodynamic type and
Nonlinear WKB.
Uspechi Math. Nauk - Russian Math Surveys, 1993, v. 48,
n.1, pp 155-156 (with A. Maltzev).
128. Hydrodynamics of Soliton Lattices. Mathematical Physics Reviews, ed by B.
Dubrovin and S. Novikov, Siviet Scientific Reviews ser C, 1993, v 9, part 4, pp
58-106 (with B. A. Dubrovin).
129. String Equation - 2. Physical Solution, Algebra and Analysis, 1994, v. 6,
n 3, pp 118-140;
130. Solitons
and Geometry. Fermi lectures 1992. Scuola Norm. Sup. di Pisa, Cambridge Univ. Press, 1994.
131. The Semiclassical Electron in a Magnetic Field and Lattice. Some Problems
of the Low Dimensional Periodic Topology, Geometric and Functional
Analysis, 1995, v. 5, n. 2, pp. 434-444.
132. Nonselfinersecting magnetic orbits on the plane. Proof of Principle of the
Overthrowing of the Cycles, Topics in Topology and Mathematical Physics, 1995,
AMS Translations (2), v. 170, 59-82, arXiv, solv-int/9501006 (with
P. G. Grinevich).
133. Exactly solvable periodic 2-d Schroedinger operators.
Russian Math.Surveys, 1995, v 50, n. 6, pp 171-172
(with A. P. Veselov).
134. Topology-1. Encyclopedia of Mathematical Sciences, Springer Verlag, 1996,
vol.12, 320 p.
135. Topological quantum characteristics observed in the investigation of
conductivity in normal metals, JETP Letters, vol. 63, n10, 25 May 1996, translated
by the American Institute of physics, (with A.Ya. Maltsev).
136. Algebraic properties of 2D difference operators.
Russia Math Surveys, 1997, vol 52, iss 1, pp 225-226
137. Discrete Spectral Symmetries of low-dimensional differential
operators and difference operators on regular lattices and two-dimensional
manifolds. Russian Math. Surveys, 1997, vol 52, iss 5, pp 175-234. arXiv, math-ph/0003009 (with I.
A. Dynnikov)
138. Laplace Transformations and Simplicial Connections.
Russian Math Surveys, 1997, v 52, n 6, pp 157-158
(with I. A. Dynnikov)
139. Schroedinger Operators on Graphs and Topology. Russian Math Surveys, 1997,
v 52, n 6, pp 177-178; math-ph/0004015.
140. Exactly solvable 2-dimensional Schroedinger opeators and Laplace
Transformations, published in AMS Translations (1997), ser 2, vol 179 -
Solitons, Geometry and Topology: On the Crossroads, pp 109-132 edited by V.
Buchstaber and S. Novikov, (with A. P. Veselov) Appendix I (S. Novikov):
Difference Analogs of the Laplace Transformations. Appendix II (S. Novikov, A.
Taimanov): Difference analogs of the harmonic oscillator. ArXiv, math-ph/0003008.
141. Role of Integrable Models in the development of Mathematics In: ''Fields
Medallist Lectures". (Eds. M. Atiyah and D. Iagolnitzer). World
Scientific, Singapore Univ. Press, pp. 202-217.
142. Topological Phenomena in Normal Metals, Uspekhi Phys. Nauk, March 1998, v
168, n 3, pp 249-258=Physics-Uspekhi 41(3) 231-239; cond-mat/9709007 (with A.Ya. Maltsev).
143. Schroedinger Operators on Graphs and Symplectic Geometry, published in the
Fields
Institute Communications vol. 24, 1999, pp 397-413. Dedicated to the 60-th
birthday of V.Arnold; math-ph/0004013.
144. Discrete Schroedinger Operators and Topology, Asian Journal of
Mathematics, December 1998, vol 2, n 4, pp. 921-934 (dedicated to the 70th
birthday of Mikio Sato); math-ph/9903025.
145. Discrete Lagrangian Systems on Graphs. Symplecto-Topological Properties.
Uspekhi Mat. Nauk=Russian Mathematical Surveys, 1999, v 54, n 1, pp 257-258; math-ph/0004011 (with A.S.Schwarz).
146. Discrete Schrodinger Operator. Published in the volume "Trudy Steklov
Math. Institute'', 1999, vol 224, pp 275-290 (dedicated to the 90th
birthday of L. Pontryagin)
147. The levels of quasiperiodic functions on the plane and Hamiltonian
systems. Uspekhi Math Nauk=Russian Math Surveys, 1999, v 54, n 5, pp 147-148; math-ph/9909032.
148. Trivalent graphs and solitons. Uspekhi Math Nauk, 1999, v 54, n 6, pp
149-150; math-ph/0004009 (with I. Krichever).
149. Periodic and almost periodic potentials in inverse problems. Inverse problems, 1999,
v.15,, p.p. R117-R141. IOP Publishing Ltd.
arXiv, math-ph/0003004.
150. Holomorphic bundles and scalar difference operators. One-point constructions.
Uspekhi Math Nauk=Russian Math Surveys, 2000, v 55, n 2, pp 159-161; math-ph/0004008 (with I. Krichever).
151. Holomorphic bundles and commuting difference operators.
Two-point constructions.
Uspekhi Math Nauk=Russia Math Surveys, 2000, v 55, n 3, pp 181-182 (with I.
Krichever).
152. The algebraic aspects of the
multiplications in the Complex Cobordisms. Uspekhi Math Nauk=Russian
Math Surveys, 2000, v 55, n 4, pp 5-24; math.AT/0103066 (with B. Botvinnik, V. Buchstaber, S. Yuzvinski).
153. I.Classical and Modern Topology. II.Topological Phenomena in Real World
Physics. published in GAFA=Geometric and Functional Analysis, 2000, Special
Volume GAFA-2000, Visions in Mathematics, Birkhauser Verlag, Basel, 2000, p.
406-425; math-ph/0004012.
154. On the local systems hamiltonian in the weakly nonlocal Poisson
brackets, 2000, presented for publication in the Journal Fisica D in July
2000, published in June 2001; nlin.SI/0006030 (with A.Ya.Maltsev);
155. Real finite-gap solutions to the Sine-Gordon equation; formula for the
topological charge.
Uspekhi Math Nauk=Russian Surveys, 2001,v.56, n.5 (with
P.G.Grinevich).
156. Topological
Charge of the real finite-gap periodic Sine-Gordon solutions. Communications on
Pure and Applied Mathematics, 2003, v. LVI, dedicated to the memory of Juergen
Moser, Wiley Periodicals Inc., arXiv, math-ph/0111039.
157. A note on the real fermionic and bosonic quadratic forms: diagonalization and
topological interpretation, arXiv,
math-ph/0110032.
158. On the exotic de-Rham cohomology. Perturbation
Theory as a Spectral Sequence, preprint, math-ph/0201019.
159. Geometry of the triangle equation on two-manifolds. Moscow Mathematical Journal, v 3(2003), pp 419-438
(this volume is dedicated to the 65th birthday of V.Arnold)(with I. A.
Dynnikov), 23 pages. arXiv,
math-ph/0208041.
160.Topological Phenomena in the Real Periodic Sine-Gordon Theory, Journal of
Math Physics, vol 44, n 8, August 2003, pp R3137-R3147,arXiv, math-ph/0303039,
(with P.Grinevich).
161. Quasiperiodic Functions and
Dynamical Systems in Quantum Solid State Physics. Bull. Braz. Math.Soc., New
Series 34 (1), pp 171-210, 2003. arXiv, math-ph/0301033
(with A.Maltsev )
162. 2-dimensional Toda lattice,
commuting difference operators and holomorphic vector bundles, Uspekhi Math.
Nauk= Russian Math. Surveys, 2003, v.58, No. 3, pp 51-88 (with I.Krichever). ArXiv, math-ph/0308019.
163. Discrete Connections on the
Triangulated Manifolds and Difference Linear Equations arXiv, math-ph/0303035. This work
is published in Proceedings of Steklov Math. Inst., v 247 pp. 186-201 (2004)
164. Dynamical Systems, Topology and Conductivity in Normal Metals, Journal of Statistical Physics,
April 2004, vol 115, iss 1-2, pp 31-46 (16), (revised in October 2003)
arXiv,
cond-mat/0304471 (with A.Maltsev).
165. Integable Systems. 1. Encyclopedia Math. Sciences, Dynamical Systems, v.4 (edited by
V.Arnold and S.Novikov), second, expanded and revised edition, pp 177-332,
Springer-2001 (with B.Dubrovin and I.Krichever)
166. Algebraic Topology. Modern Problems of Mathematics.
(Steklov Math Institute Series, founded in 2003),pp 1-46 (in Russian)
A revised version of this article is published: Topology in the XXth Century:
A view from inside. Uspekhi Math. Nauk=Russian Math Surveys, vol 59 (2004). n 5
167. On the metric independent exotic homology, preprint,
arXiv, math.DG/0403452
This work was published in the Proceedings (Trudy) of the Steklov Math Institute,
vol. 251 (2005), pp. 202-212
168. Topology of the quasiperiodic functions on the plane and dynamical systems.
Uspekhi Math. Nauk, 2005, v. 60. n 1
arXiv:math.0410464 (with I. Dynnikov)
169. Topology of foliations given by the real parts of holomorphic 1-forms.
arXiv, math.GT/0501338
(v1 - 21 Jan 2005, revised - February, 10, 2005 and March 31, 2005).
170. Topology of the Generic Hamiltonian Foliations on the Riemann Surface.
Math.GT/0505342. New version. This work was published in the Moscow Math.
Journal (MMJ) , vol 5 (2005), n 3, dedicated to the 70th birthday of
Ya.G.Sinai, pp 633-667
171. Dynamical Systems and Differential Forms. Low Dimensional Hamiltonian Systems.
arXiv, math.GT/0701461.
Contemporary Math., 469 (AMS), vol. Probabilistic and geometric methods in Dynamical systems
(K.Burns, D.Dolgopyat,Ya.Pesin, eds.), in honor of M.Brin
172. S.Novikov, I.Taimanov. Modern Geometric Structures
and Fields. Graduate Studies in Mathematics, vol 75, AMS, Providence, Road
Island.
173. New discretization of complex analysis. The Euclidean and hyperbolic planes.
arXiv:0809.2663
174. Four Lectures: Discretization and Integrability. Discrete
Spectral Symmetries. Newton Institute for Math Sciences, Cambridge
University, UK, August 8-20, 2001, Special Semester dedicated to the
Completely Integrable Systems and Solitons, Fall 2001. Published in
the special volume (A.V.Mikhailov, editor), Springer Verlag, 2008.
175. Lectures on Discrete Systems, University of Montreal, Canada,
June 13-20, 2008, to appear in the Proceedings of Workshop on the
Discrete Systems and Symmetry.
176. Singular finite-gap operators and indefinite metrics. I.
arXiv:0903.3976
(March 2009, with P.Grinevich). Uspekhi Matematicheskih Nauk,
2009, v. 64, no. 4, p.p. 45–72
Additional items:
a) $ 10. A theorem of S.P.Novikov. Included in the article:
I.Volodin, V.Kuznetsov, A.Fomenko. The problem of discriminating algorithmically
the standard three-dimensional sphere. Russian Mathematical Surveys, 1974, v. 29, no. 5,
p. 169-171.
b) "Novikov-Veselov's Quasicrystallographic Groups". Included in the article: Le Tu Thang, S.Piunikhin, V.Sadov. The Geometry of Quasi-Cristals
Russian Math. Surveys (1993), vol. 48, n 1, pp 37-100 - see page 46 (in Russian).
c) The Morse Theory and von Neumann invariants of non-simply-connected
manifolds (in Russian);
The Morse Theory and von Neumann invariants of non-simply-connected
manifolds (translation from Russian with the present authors comments),
Uspekhi Math Nauk=Russian Math Surveys, 1986, vol. 41, n 5, pp.
222-223 (in Russian), Section of Mathematical Life in USSR: Meetings of the
I.G.Petrovski Seminar in Differential Equations and Mathematical Physics,
March 5 1986, 1st meeting, (with M.Shubin)
The Series of Public Speeches and Essays under the General Title
Mathematicians behind the Iron Curtain
In Russian
1. ''Mathematicians and Physicists in the Academy
in 60s-80s'' (published in the book ''Collection of Memoirs on the academician M.A.
Leontovich'', second edition (extended), Moscow, Nauka, PhysMatLit 1996, pp.
354-369, in Russian, third edition in 2003, and in the Transactions of the Institute for the History
of Natural Sciences and Technology, Moscow, 1995).
2. ''Problems of Math Education in Russia''
(published in the Transactions of the Institute for the History of Natural Sciences
and Technology, 1997, N 1, pp. 97-106).
3. ''Mathematicians and History''
(published in the popular journal ''Priroda'', 1997, n 2, pp 70-74, in Russian; this is a
short version of the unpublished but widely distributed article
''Mathematicians are the Gerostrats of the History'').
4. ''Rokhlin'' (published in the special volume: V.A.Rokhlin.
Selected Works. Independent University of Moscow,
1999, pp. 472-491).
5. ''Pseudomathematics and pseudohistory. Fantastics in our life.'' (Published in
Uspekhi Math Nauk=Russia Math Surveys, 2000, v 55, n 2, pp 159-161.)
6. Interview with S.P.Novikov (made by V.Buchstaber),
American Math Society Translations ser 2 vol 212, 2004, pp. 25-40 (in
English)
7. ''An academy tale on the
A.D.Alexandrov: Danilych''. Published in the special volume, dedicated to the memory of
A.D.Alexandrov, 2001. According to the personal request of
O.A.Ladyzenskaya, section II was dropped in the memorial edition. This
text contains it.
8. The Second Half of the 20th Century and its Conclusion: Crisis of the
Physics and Mathematics Community in Russia and in the West
Published in the Transactions of the Institute for the History of the Natural Sciences and
Technology, 2002(in Russian and in English). Published by the Institute for the History of the Natural Sciences and
Technology, Istorico-Matematicheskiye Issledovaniya, vol 7(42)(2002) pp 326
356 (in Russian). English translation made by A.Sossinsky is published in the volume: AMS
Translations (2) vol 212 (2004) pp 1-24 , S.P.Novikov's Seminar, 2002-2003
(edited by V.Buchstaber and I.Krichever).
9. The most signifiant Public Speeches of S.Novikov in the General
Meetings of the Academy of Sciences of USSR/Russia:
a) General Academy Meeting, October 1988, "The Situation in the Moscow
State University and the activity of its rector against the Einstein General
Relativity”.
Published in Vestnik of the USSR Academy, 1989, n 2, pp 81-82
b) General Academy Meeting, May 1997, "On the role of Shiryaev in
the creation of the new branch of the Russian but not International Applied
Mathematical Statistics– Mathematical
Pseudohystory” (unpublished)
c) General Academy Meeting, March 1998, "On the scientifically incompetent
activity of Fomenko in the Applied Mathematics and Pseudohystory",
read by the President of Academy on the General
Academy Meeting, March
26, 1998, the pieces of this speech were published on the titlepage of the
Journal Uspekhi Math Nauk, 1998, v 53, n 5, Russian edition
10. On the Policy of Editorial Board of the Journal Uspekhi Math
Nauk/Russian Math Surveys (UMN/RMS) in the period of rapid changes.
Russian Math Surveys (2009), vol 64 n 5, pp 189-191.
11. Applied Mathematics and
Applications of Mathematics. Inaugural Address (AMAM, Nice, February 10-15,
2003). EMS Newsletter # 54, December 2004, p.9-10.