Novikov, Sergei Petrovich                                                                                     Updated: January 2012

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, Magnetoresistance 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
Scientific Publications (to see all scientific works of S.P.Novikov please click ''Scientific Publications'' here. The lists of publications of S.P.Novikov presented in the systems MathSciNet and MathNetRu include huge number of nonscientific publications including Novikov's name in the list of editors, the author of forewords and a lot of biographical articles dedicated to various anniversaries, jubileums and coauthor of memorials of mathematicians signed sometimes by many colleagues. In particular the so called Erdos number made on the base of these lists make no sence. To see the full list of publications of S.P.Novikov on MathNetRu click here).
Conferences attended by S.Novikov in 1959-1970 (working in Topology)
Conferences and Talks in 1971-1991 (Interacting with Physics Community)
Conferences and talks in 1991-1996 (floating in the Free Word)''
Full list of Novikov's Talks since 1997
Recent talks
Full list of Novikov's courses at the University of Maryland for the period 1996--2014
Russian mathematicians in the 20th century. Memoirs. Essays. Public Speeches.

Vita and Education:

Born: March 20, 1938, Gorky City (N. Novgorod),
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).

Employment:

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"

Special Service:

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
2008-2010 Member of the Abel Prize Committee

Awards and Honors:

1964- Moscow Math Society Award for young mathematicians
1966-1981 Corresponding member of the Academy of Sciences of the USSR
1967 - Lenin Prize
1970 - Fields Medal of the International Mathematical Union
1981 - Lobachevskii International Prize of the Academy of Sciences of the USSR
1981 - Full Member of the Academy of Sciences of the USSR
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
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, University of Tel Aviv.

2003 – Fellow, European Academy of Sciences, Brussels
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
2010, September 14 - Elected Honorary President of Moscow Math Society by the General Meeting of Society
2011 - Elected a Honorary Member of the Montenegro (Chernogoria) Academy of Art and Sciences
2012 - Euler Medal of the Russian Academy of Sciences

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''

The Scientific School:

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.

Scientific Results

Many important works of S.Novikov were done in collaboration with his pupils; some of them became outstanding scientists working in different areas. All scientific results in the works published with collaborators, equally belong to all authors, if opposite is not written directly in the paper. Concerning new scientific results: the order of authors is always purely alphabetical in the language and alphabet of the original publications (there are some exceptions for survey articles, monographs and textbooks but not for new scientific results).

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 the section 10. A theorem of S.P.Novikov
published in Uspekhi Math Nauk=Russian Mathematical Surveys (1974): see the copy of this piece in Publications, Additional Item - below

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). The Ring Structure of the Stable Homotopy Groups of Sheres was used to find the first proof that The Connectivity Component of Unit in the Diffeomorphism Groups of some spheres cannot be deformed to the orthogonal subgroup (1962-63) for n=7 and more. Let us remind that the existence of nontrivial components was discovered by Milnor in 1956 for n=6.
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 theta-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, 2008-2009, 2011)

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, with P.Grinevich)

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). Recent results: Full Spectral Solution of the reduction problem for the factorized 2D Schrodinger Operators and corresponding 2D Soliton Hierarchy was found. It turns out that it is a 2D ''Burgers Hierarchy''. The Algebrogeometric Theory of the Ground State of the 2D Supersymmetric (i.e.Magnetic) Pauli Operators was constructed on that base (with Grinevich and Mironov, 2010-2012).

Discrete Systems:
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:
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).

Publications:

Scientific Works, Survey Articles, Textbooks
and
Popular Articles in Mathematics and Math Physics  [2]

1. Cohomology of the Steenrod algebra. Dokl. Akad. Nauk SSSR, 1959, v. 128, N 5, 893-895 (submitted 29.05.1959).
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., Stockholm, 1962, section 4, 139.
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. Main trends of algebraic topology and algebraic geometry, Uspekhi Mat. Nauk, 1964, v. 19, N 6, 75-82 (with I. I. Pyatetskii-Shapiro and I. R. Shafarevich).
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 manifolds I. Izv. Akad. Nauk SSSR, 1965, v. 29, N 6, 1373-1388.
22. Structures on manifolds, Proc. 4th All-Union Topology Conference (Tashkent 1963), 1965, 90-120.
23. The topology of foliations, Trudy Moskov. Mat. Obshch, 1965, v. 14, 248-278.
24. On manifolds with free Abelian fundamental group and their applications. Izv. Akad. Nauk SSSR, 1966, v. 30, N 1, 207-246. The translation has been made by AMS in 1968, s. 2, v. 71 (1968), pp. 1-42. This article also has been translated recently in the Topological Library v 2. As far as I know the work of Siebenmann mentioned in the footnote at the page 38 never has been published
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 I. R. Shafarevich).
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, Kiev, 1968, v. 3, 511-529 (with A. M. Vinogradov).
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, New York, 1970, 147-155.
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, Paris, 1971, vol. 2, 39-45.
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 I. M. Krichever).
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, Moscow State University, M. 1978 (with A. S. Mishchenko, Yu. P. Solov'ev and A. T. Fomenko).
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, Moscow State University, M. 1978, 184-185.
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, Moscow, 1979 (with B. A. Dubrovin and A. T. Fomenko).
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 I. M. Krichever).
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, Moscow, 1979, 164-176 (with O. I. Bogoyavlenskii).
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, Moscow, 1980 (with V. E. Zakharov, S. V. Manakov, and L. P Pitaevskii).
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 I. M. Krichever).
99. Two-dimensional periodic Schroedinger operators and Prym's q-functions, in Geometry Today, Internat. Conf. Rome, June 1984, Boston, 1985, 106-118 (with A. P. Veselov and I.M. Krichever).
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, Moscow 1986 (with B. A. Dubrovin and A. T. Fomenko).
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, Moscow, 1987 (with A. T. Fomenko).
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 I. M. Krichever).
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 I. M. Krichever).
111. Virasoro-type algebras, Riemann surfaces and strings in Minkowski space, Funktsional. Anal. i Prilozhen., 1987, v. 21, N 4, 47-61 (with I. M. Krichever).
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 I. M. Krichever).
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, Singapore, 1990, 356-388 (with I. M. Krichever).
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, Kyoto, Japan, pp 293-300
121. Hydrodynamics of the Soliton Lattices and Differential Geometry. (Collection of the survey articles. Potsdam. 1992, edited by A. Fokas.)
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. Springer-Verlag, New York.
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). Houston, TX Publish or Perish, 1993, 223-233.
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;
solv-int/9501002 (with P. G. Grinevich).
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. Four Lectures on Discrete Systems ( Summer School on Integrability of Difference Equations at Montreal, June 2008) published in the book ''Symmetries and Integrability of Difference Equations'', London Math Society, Cambridege University Press ( edited by D.Levi, P.Olver, Z.Thomova, P.Winternitz).
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
177. New Reductions and Nonlinear Systems for 2D Schrodinger Operators, arXiv math 1001:4300 (with P.Grinevich and A.Mironov)
178. Zero level of purely two-dimensional magnetic nonrelativistic Pauli operator for spin=1/2 particles, Theoretical and Mathematical Physics, 2010, 164:3, 1110-1127 arXiv:1004.1157 (with P.Grinevich and A.Mironov)
179. 2DSchrodinger Operator; (2+1) Evolution Systems and Their New Reductions. The 2D Burgers Hierarhy, arXiv:1005.0612 and Russian Math Surveys, 2010, v 65, n 3, p. 580-582 (English) (with P.Grinevich and A.Mironov)
180. Erratum. Theoretical and Mathematical Physics, 2011, 166:2, p. 277 (with P.Grinevich and A.Mironov)
181. On the nonrelativistic 2D Purely Magnetic Supersymmetric Pauli Operator. Arxiv:1101.5678 (with P.Grinevich and A.Mironov). New extended version (19 Dec 2011) see in arXive.
182. Singular Solitons and Indefinite Metric. Arxiv:1103.2505, version 3 (with P.Grinevich). A version of this work appeared also in Doklady Academii Nauk, 2011, v 436, n 3, pp.302-305 (in Russian) and Doklady Matematiki, 2011, v. 83, n.1, pp. 56-58 (in English). New extended version (1 Jan 2012) see in arXive.
183. 2D Pauli operator in the magnetic field. Low temperature physics, 2011, v. 37, pp. 829-833 (with P.G.Grinevich and A.E.Mironov). Russian version: "Dvumernyi operator Pauli v magnitnom pole" -- Fizika nizkih temperatur, 2011, t. 37, n. 9-10, s. 1040-1045;
184. Singular Soliton Operators and Indefinite Metric. (with P.Grinevich). Arxiv:1103.2505 (under slightly different title). To appear in the Bulletin of Brasilian Math Society, 2013, special issue dedicated to the 60th Anniversary of IMPA
185. Discrete SL2 Connections and Self-Adjoint Difference Operators on the Triangulated 2-manifold Arxiv:1207.1729 (with P.Grinevich).
186. MATH740, Maryland, Spring 2014, Graduate Course ''Fundamental Concepts of Riemannian Geometry and Topology of Manifolds''
187. Topology from the Differential point of view. Program of Course given in Maryland, Fall 1996
a) $10. A theorem of S.P.Novikov. Included in the article: I.Volodin, V.Kuznetsov, A.Fomenko. The problem of discriminating algorithmically the standard three-dimensional sphere. Russian Mathematical Surveys, 1974, v. 29, no. 5, p. 169-171. b) "Novikov-Veselov's Quasicrystallographic Groups". Included in the article: Le Tu Thang, S.Piunikhin, V.Sadov. The Geometry of Quasi-Cristals Russian Math. Surveys (1993), vol. 48, n 1, pp 37-100 - see page 46 (in Russian). c) The Morse Theory and von Neumann invariants of non-simply-connected manifolds (in Russian); The Morse Theory and von Neumann invariants of non-simply-connected manifolds (translation from Russian with the present authors comments), Uspekhi Math Nauk=Russian Math Surveys, 1986, vol. 41, n 5, pp. 222-223 (in Russian), Section of Mathematical Life in USSR: Meetings of the I.G.Petrovski Seminar in Differential Equations and Mathematical Physics, March 5 1986, 1st meeting, (with M.Shubin) Conferences attended by S.Novikov, 1959-1970 (working in Topology) 1. Conference in Topology, Tbilisi, September-October 1959. Made talk dedicated to the Study of Ring of the Stable Homotopy Groups of Spheres by the Adams Spectral Sequence based on the Homological Algebra for the Graded Cocommutative Hopf Algebras over the finite fields including analog of the Steenrod Operations. 2. Conference in Algebra, Uzgorod, October 1959. Made talk dedicated to the attempt to construct analog of the Adams Spectral Sequence for the Unstable Homotopy Groups (unpublished). 3. All-Union Math Congress, Leningrad, June 1961. Made Invited Talk in the Section of Topology exposing the Recent Solution of Multidimensional Poincare' Conjecture by Smale, Wallace and Stallings. 4. International Math Congress, Stockholm, August 1962. Presented a contributed talk to the section of Topology dedicated to the diffeomorphism classification of multidimensional ($n>4$) simply-connected manifolds (was not allowed to travel by the Soviet Academy authorities; talk was presented by W.Browder). 6. Conference in Topology, Tashkent, Fall 1963. Made invited Plenary Talk ''Structures in Topology'' (including new results in foliations). 7. Gorki School in Topology, Gorki (N.Novgorod), Summer 1964. Made series of lectures in Topology for the Experts in Topology, Algebra, Analysis, PDE, Dynamical Systems. 8. School in Topology, Druskininkai, Summer 1965. Made series of lectures in Topology for the students and experts in other areas of mathematics. 9. International Conference in Complex Analysis, Erevan, September 1965. Presented new result to H.Cartan and M.Atiyah ( Proof of Topological Invariance of Rational Pontryagin Classes). 10. International Math Congress, Moscow, August 1966. Made Invited Section Talk dedicated to the Algebraic Topology Methods based on the Complex Cobordism Theory replacing the originally presented subject. 11. Visited US in May-June 1967: Princeton, New-York, Chicago, Boston, New Orleans and nearby Tulane Conference in Topology and Group Actions, San-Francisco, Los-Angeles. Made several talks (Classification of Manifolds, Complex Cobordisms and Formal Groups, Topological and Homotopy Invariance of Pontryagin Classes, Foliations). 12. Attended Topological Conference in Novosibirsk, July 1967. Made talk in the Differential Topology. Visited Tbilisi, September 1967. Made series of lectures for the Students. Made lecture in the Moscow Math Society about new ideas in Topology in USA, especially concerning Arf-invariant Problem (W.Browder) and Analytical Reidemeister Torsion (I.Singer) about 3 years before these results were finished and published by the authors. 13. Attended Voronez Winter School, January-February 1968. Made series of lectures for mathematicians of different areas. During this school some person impersonated S.Novikov in Moscow, Kiev and some other cities (it turned out that this person was originated from Kiev. He impersonated also academician Flerov. Claimed mental sickness after being approached by militia). 14. International Congress in Math, Nice, France, August 1970, Awarded by the Fields Medal. Soviet Academy and Steklov Institute Authorities did not allowed to travel. Presented the Invited Talk in the Section of Topology ''Hermitian Analogs of the K-Theory''. In particular, the so-called ''Novikov Conjecture'' was formulated. Actually, talk was read by A.Miscenko. 15. Made talk in Moscow Math Society concerning various applications of Formal Groups in Topology, Winter 1971. Conferences and Talks, 1971-1991. Interacting with Physics Community. 1. Conference in Topology, Tbilisi, Fall 1972. Made Plenary Lecture about the Homogeneous Cosmological Models near singularity based on the General Relativity. Their Dynamics, Geometry and Topology is studied by the methods of Qualitative Dynamical Systems. 2. Workshop in the Inverse Scattering Transform, Ufa, November 1973. First approach to the Modern Theory of Solitons. 3. Visited Dushanbe, Tadjikistan, December 1973. Made lecture in the Tadjik Academy on the Cosmological Models. Made lectures in the same subject in the Landau Institute Seminar, Chernogolovka, in the Moscow Math Society and in the Steklov Institute General Seminar. 4. Moscow, I.G Petrovski Seminar in PDEs and Math Physics, February 1974. Made talk presenting new results in the Periodic Theory of Solitons (KdV) and Finite-Gap Potentials. Made similar talks in the Moscow Math Society and Landau Institute Seminar. During the period 1974-75 visited several places and made talks in the same subject (in particular, in Kharkov Math Society chaired by N.Akhiezer and Kiev Academy Institute for Theoretical Physics chaired by N.Bogoliubov). 5. Moscow, First Joint Meeting of the Moscow Math Society and I.G.Petrovski Seminar, MSU, January 1976 (dedicated to the 75th birthday of Petrovski). Acted as a chairman of the Special Section ''Theory of Solitons and Topology''. Made Plenary Talk about New Completely Integrable Systems associated with 2D 2nd order Schrodinger Operators and Inverse Problems based on the selected energy level. Worked as a Chairman of that Section every year since 1976 for all January Joint Meetings of MMS and Petrovski Seminar. Made Plenary Talks at all January Meetings up to the Year 1990. 6. Conference in Math Physics, Warsaw, Poland, Spring 1976 Made talk about Dynamical Systems and Cosmological Models. Visited Vienna, Austria at the Fall 1976. Made talk in the same subject. 7. International Congress in Math Physics, Rome, July 1977 Made invited Plenary Talk about the Periodic Theory of Solitons. (This Lecture was not presented for publication in the Congress Proceedings) Attended the Satellite Conference in the Theory of Solitons, Rome, July 1977. Made talk in the same subject. 8. International Congress in Mathematics, Helsinki, Finland, August 1978. Made Plenary Talk about the Methods of Algebraic Geometry in the Theory of Completely Integrable Systems and Spectral Theory of Periodic Operators. 9. Visited Rome, Pisa and Torino, June 1979. Made talks in the General Relativity (Torino) and Completely Integrable Systems (Rome) Formulated the connection of Soliton Theory with classical Riemann-Shottki Problem for Theta-Functions making talk in the Seminar in Scuola Mormale Superiore di Pisa chaired by Andreotti. 10. Conference on fundamental problems in Math and Theor Physics, Dubna, Summer 1979. Made talk ''Algebraic Geometry and Math Physics'' (dedicated to the 70th birthday of Bogoliubov). 11. USSR-USA Workshop in the Theory of Solitons, Kiev, September 1979. Made talk dedicated to the theory of Higher Rank Solution to the KP Equation and Commuting Operators. 12. Attended Conference in Statistical Mechanics, Dubna, Summer 1981. Made Talk about the Ground States of the Purely Magnetic 2D Nonrelativistic Pauli Operator. 13. International Congress in Math Physics, West Berlin, Summer 1981. Made invited Plenary Talk about the New Calculus of Variations (Field Theory) with Multivalued Action (which is a closed one-form) leading to the Topological Quantization of Coupling Constant in process of path integral quantization. It generated also new areas of Topology and Morse-Type Theory (The Morse-Novikov Theory). This talk was not presented for publication in Proceedings (it was already published by the author). 14. Attended Conference in Analytical Mechanics, Torino, Summer 1982. Made talk about Multivalue Variational Principle in Mechanics, Physics and Geometry. It was revealed how effective ''Monopole Type'' Magnetic Fields appears out of Factorized Poisson Structures for the Top in the Perfect Liquid. 15. Attended Joint Annual Workshop of the ''Landau-Nordita'' Institutes, Kopenhagen, September-October 1982. Made talk about finite-gap periodic operators and their applications in solid state physics. 16. Attended Joint USSR-Poland Workshop in Math Physics, Banach Institute, Warsau, December 1983. Presented Lecture in the Theory of Hydrodynamic Type Systems. 17. {Attended joint Workshop Landau Inst.-Rome University, Rome, June 1884. Made talk in the Theory of Solitons. Visited Torino. Made talk about Multivalued Action Functionals and Classification of the Local Cases. Attended Conference ''The Days of Geometry'' (Giornate di Geometria), Rome, June 1984. Made talk about 2D Schrodinger Operators with zero magnetic field and Prym's Varieties. 18. Attended Conference in Statistical Physics, Dubna, Summer 1984, in honor of 75th birthday of Bogoliubov. Made talk about new ideas developing Bogoliubov-Whitham averaging method in the Theory of Solitons: The Hamiltonioan Theory of Hydrodynamic Type Equations and Riemannian Geometry. 19. Second USSR-USA Workshop in the Theory of Solitons, Kiev, Fall 1984. Made Talk about new developments in the (2+1 ) Theory of Solitons and Algebro-Geometric Schrodinger Operators without Magnetic Field. The Prym's Theta functions. 20. Participated in the Conference dedicated to the 50th Anniversary of Steklov Institute, Moscow-Leningrad, Fall 1984. Made talk about the Hamiltonian Type Poisson Brackets on the Loop Spaces and their Generalizations. 21. Visited Brasil, Rio da Janeiro, IMPA, and San Paulo, June 1985. Made lectures in IMPA about Multivalued Functionals and Theory of Solitons. 22. International Congress in Math Physics, Marseille, Summer 1986. Made Plenary Talk about the 2D Schrodinger Operator and Soliton Systems. 23. Participated in the 100th Anniversary Conference of I.Schrodinger, Imperial College, London, Summer 1987. Made talk about applications of Quantum Mechanics in the Theory of Nonlinear Waves. Visited several Universities in UK--Oxford, Cambridge, Edinburgh and others. Made several talks about the Periodic Theory of Solitons and Algebraic Geometry, Hamiltonian Hydrodynamic type systems and Riemannian Geometry. 24. Participated in the Conference dedicated to the 80th birthday of I. Vekua, Tbilisi, Fall 1987. Made invited Lecture about the applications of Generalized Analytic Functions in Theory of Solitons and in the Inverse Spectral Problem for the 2D Schrodinger Operators with Rapidly Decreasing Potential and zero Magnetic Field. Solution of the Big Norm Problem for the levels below the ground state. 24. International Congress in Math Physics, Swansea, UK, Summer 1988. Made Plenary talk about the applications of Baker-Akhiezer-Type Functions and Tensor Fields on Riemann Surfaces for the construction of Operator Quantization of the Multiloop Interacting Bosonic String Theory. This talk was not presented for publication in the Proceedings of the Congress (this material was already published in the Journal). 25. Attended J.Moser 60th birthday Conference, Zurich, August 1988. Made talk about the Hamiltonian Theory of Hydrodynamic type systems and Riemannian Geometry. 26. Visited US in October 1988, participated in the Joint USA-USSR Workshop in New York, visited Philadelphia, Boston. Made several lectures about the Operator Quantization of Strings based on the ideas of the Soliton Theory. 27, Visited Spain, Summer 1989: Madrid, Sevilla, Grenada, Barcelona, Bilbao and other cities. Made several lectures in Topology, Morse-Type Theory and Theory of Solitons. 27. Attended Topological Conference in Tbilisi, September 1989. Made Talk about the Morse-Type Theory. 28. Attended Conference in l'Aquila, Italy, January 1990. Made Talk about periodic orbits in Magnetic Field homotopic to zero. Visited Rome University. Made talk about news in the Theory of Solitons. 29. Attended Workshop in Kyoto, May 1990. Made lectures about the Operator Quantization of Bosonic Strings. Presented new approach to the study of the matrix-model based ''String Equation''. Visited Tokio, May 1990.) Made talk about String Equation. 30. Visited Tel-Aviv University and Hybro University of Jerusalem, December 1990-January 1991. Made lectures in the Morse-Type Theory and Theory of Solitons. 31. Worked in Highest Normal School of Paris, Laboratory of Theor Physics, February -August 18, 1991. Attended Meeting of Fields Medallists, Barcelona, June 1991, Conference dedicated to the 60th birthday of J.Milnor, Stonybrook, USA, July 1991. Conference in Marseille, July 1991, Conference in Lyon, July 1991 and Workshop in Corsica, Cargese, August 1991. Made General Talk in Barcelona, Presented several lectures at the Milnor Conference about Periodic Soliton Theory and Riemann Surfaces, made talks in Lyon and Marseille about Hamiltonian Hydrodynamic Type Systems, Dispersive Shock Waves. Made talk about String Equation in Corsica. Returned from France exactly when the G-K-CH-P Coup was started, and USSR ended its existence. Conferences and Talks, Fall 1991-1996. Looking around in the free world. 1. Moscow State University Moscow Math Society. President of MMS from 1985 to 1996. Made Annual Scientific Lecture about the current research every year in December or January 2. Visited Unified Germany, (former) W.Berlin, November-December 1991. Made talks about Topology of Integrable Systems, Theory of String Equation and Theory of Solitons. 3. Worked as a visiting professor, USA, University of Maryland, College Park, January-May (Spring Semesters) 1992, 1993, 1994, 1995, 1996. Made several Topics Courses in the Theory of Completely Integrable Systems, Symplectic Geometry and Topology in Mathematics and Physics, Modern Theory of Knot Polynomials, Topology from the differential point of view, Algebraic Topology and others. Visited many US universities and made many talks about the current scientific results and general survey lectures. 4. Visited Italy, Scuola Normale Superiore di Pisa, June 1992. Made series of lectures (The Fermi Lectures) dedicated to the Theory of Poisson Structures with applications to the study of Hydrodynamic Type Systems. Special attention was given to Poisson Structures on the Loop Spaces and Riemannian Geometry (Published as a minibook in 1994). 5. Visited S.Korea, Seoul and several other universities in Korea, 1993. Made several lectures about recent results. 6. Visited Canada, Toronto, Fields Institute and University, Spring 1994. Made General Lecture 7. Visited Paris, Summer 1994, group of C.Bardos and F.Golz. Made series of lectures about Hamiltonian Hydrodynamic Type Systems 8. Visited Milan, Italy, Fall 1994. Made Leonardo da Vinci Lecture ''Algebraic Geometry and Math Physics'' 9. Attended Conference in Israel, Tel Aviv University, December 1994. Made talk about the Motion of Electrons along Fermi Surface in the Solid State Physics, 3D Topology and Dynamical Systems 10. Visited Itali, Como, first ''Landau Network'' Workshop, May-June 1995. Made talk about the Theory of ''String Equation'' (i.e.special solutions to P1 equation) Full list of Novikov's Talks since 1997. Only talks made in Novikov's Seminar in Steklov/MSU are not included here: there are no records to make list of them: 1997: January 5-25, France, Paris, University of Paris-VII. Made 2 lectures in the Math Physics Seminar: Lecture 1: Laplace transformations and Exactly Solvable 2D Schrodinger Operators Lecture 2: Topological Phenomena in the 3D Normal Metals in the Strong Magnetic Field March 7-9, Germany, Berlin, (visited Germany as a Member of the Program Committee of The International Mathematical Union). Made a lecture at the ''Technische Universitat'' , Seminar in Math Physics; Lecture: Topological Phenomena in 3D Normal Metals April 15, USA, Baltimore, John Hopkins University. Made a lecture in the Topological Seminar Lecture: Low Dimensional Topology and Normal Metals May 20, Russia, Moscow, Moscow Math Society Lecture Lecture: Laplace Transformations and Exactly Solvable 2D Schrodinger Operators June 1, Russia, Moscow State University, Conference in Condensed Matter Physics, dedicated to the 90th birthday of I.Lifshitz, Made Invited Plenary Lecture Lecture: Lifshitz Ideas and Topological Phenomena in Normal Metals June 12-27, UK, London, Oxford, Edinburgh and Cambridge Universities. Made 2 lectures: Lecture 1: Topology and Normal Metals Lecture 2: Exactly Solvable Schrodinger Operators December 15-23, Israel, Tel Aviv University, Conference ''Entire Functions in Modern Analysis'', dedicated to B.Ya.Levin, Made Invited Plenary Talk Lecture: Discrete Symmetries of Low Dimensional Schrodinger Operators. Schrodinger Operators on Graphs. 1998: January 5, Russia, Moscow, Moscow Math Society Lecture Lecture: Schrodinger Operators on Graphs, Topology and Symplectic Geometry January 12-23, Portugal, Lisbon, Universidade de Lisboa, Grupo do Fisica Matematica, Superior Institute of Technology and C.Gulbekian Foundation Cycle of Conferences: Dialogues between Physics and Mathematics. Made 2 lectures Lecture 1: Observable Topological Phenomena in Metals Lecture 2: Schrodinger Operators on Graphs and Symplectic Geometry February 25-27, USA, Detroit, Wayne University, Meeting dedicated to Yu.Rodin, Made a Lecture Lecture: Analysis on Riemann Surfaces and Works of Yu.Rodin March 26-28, USA, Kansas-Manhattan, AMS Meeting, Made a Section Talk Lecture: Graphs and Symplectic Geometry April 4, USA, Philadelphia, Temple University, AMS Meeting, Made a Section Talk: Lecture: Hamiltonian Hydrodynamic Type Systems and Riemannian Geometry. May 26-31, Russia, Moscow, Steklov and Landau Institutes, Conference in Honor of S.Novikov's 60 birthday, made a lecture: Lecture: 3D Topology and Conductivity in Normal Metals June 10-21, Korea, Seoul, KIAS, made 3 lectures Lecture 1: 3D Topology and Conductivity in Normal Metals Lecture 2: Schrodinger Operators on Graphs and Symplectic Geometry Lecture 3: Exactly Solvable Models and Physics July 22-August 12, Italy, Trieste, SISSA, made 3 lectures Lecture 1: 3D Topology and Normal Metals Lecture 2: Schrodinger Operators on Graphs and Symplectic Geometry Lecture 3: Discrete Symmetries of Low-Dimensional Schrodinger Operators September 18-19, UK, Edinburgh, International Center for Math Sciences, Spitafield Day Lectures, Made a lecture Lecture: Observable Topological Quantities in the Conductivity of Metals September 24-26, USA, College Park, Conference ''Geometry and Solitons: On the Crossroads'' in honor of S.Novikov, Made a lecture Lecture: Topology and Conductivity of Normal Metals in the Strong Magnetic Field October 6-8, USA, Columbus, Ohio State University, made Math Colloquium Lecture: Operators on Graphs and Symplectic Geometry November 7, USA, New York University, Courant Institute, made talk at the Conference Lecture: Schrodinger Operators on Graphs and Symplectic Geometry November 9, USA, Rutgers University, I.Gelfand's Seminar, made talk Lecture: Schrodinger Operators on Graphs 1999: January 12-22, Israel, Tel Aviv University, Made talk at the University Seminar Lecture: Schrodinger Operator on Graphs and Symplectic Geometry February 17-20, Mexico, Mexico City, FENOMEC workshop, made talk: Lecture: Topological Phenomena in Metals February 22-29, USA, Berkeley, University of California, MSRI workshop, made talk Lecture: Schrodinger Operator on Graphs and Symplectic Geometry March 19-21, USA, Alabama, Birmingham, University of Alabama, Conference talk Lecture: Topological Quantities in Normal Metals May 26-June 1, Israel, Doctor Honoris Causa of Tel Aviv University, made lecture in Haifa at the meeting of the Israeli Math Union Lecture: Topology and Theory of Metals June 16-21, Germany, Berlin, Technische Universitat, made talk at the Conference (Volkswagen-Project): Lecture: Schrodinger Operators on Graphs and Topology July 5-12, Austria, Vienna-Matrei, The Erwin Schrodinger Workshop on Spectral Theory, made talk Lecture: Schrodinger Operators on Graphs and Symplectic Geometry August 3-12, Russia, Moscow, Chernogolovka, Landau Institute, Conference in honor of V.Zakharov's 60th birthday, made talk Lecture: Topological Phenomena in Normal Metals August 25-30, Israel, Tel Aviv University, Conference ''Visions in Mathematics, made talk Lecture: Topology and Conductivity of Metals. History of Topology. October 10-14, USA, Columbus, Ohio State University, Conference in Functional Analysis in honor of B.Mityagin, made talk Lecture: Schrodinger Operators on Graphs and Symplectic Geometry October 29-31, USA, Arizona, Tucson, Conference on the Complete Integrability in Math and Phys Sciences, in honor of V.Zakharov, made Plenary Talk Lecture: Solitons and Riemann Surfaces 2000: March 3-8, Germany, Berlin, Conference ''Differential Geometry and Quantum Physics, made talk Lecture: Discrete Integrable Systems March 17-19, USA, San Antonio, TX, Conference: General Topology and Dynamical Systems-Spring 2000, made talk Lecture: Quasiperiodic Functions on the Plane and Topology May 1-2, USA, New York, City University, D.Sullivan Seminar, made talk Lecture: Conductivity of Metals, Dynamical Systems, Topology May 17-23, Israel, Haifa, Technion Institute, Pollack Distinguished Lectures Series Lecture 1: Conductivity of Metals and Topology Lecture 2: Schrodinger Operators on Graphs and Symplectic Geometry Lecture 3: Discrete Symmetries of the Low-Dimensional Schrodinger Operators June 10-July 11, Korea, Seoul, KIAS, Visiting Distinguished Professor, Made Colloqium and 3 KIAS Lectures Colloquium: Topological Phenomena in the Conductivity of Metals KIAS Lectures: Lecture 1: Schrodinger Operators on Graphs and Symplectic Geometry Lecture 2: Discrete Spectral Symmetries of the Low-Dimensional Schrodinger Operators Lecture 3: Soliton Theory and Riemannian Geometry October 5-8, USA, Madison, University of Wisconsin, made talk Lecture: Schrodinger Operators on Graphs and Topology November 3-5, USA, New York, AMS Meeting, Plenary Talk Lecture: Schrodinger Operators on Graphs and Symplectic Geometry December 16-18, USA, Princeton University, Conference in Honor of Ya.Sinai and D.Ruelle, made Plenary Talk Dynamical Systems and Conductivity Theory: Topological Phenomena December 27, Russia, Moscow Math Society Lecture Lecture: Discrete Integrable Systems 2001: February 25-27, USA, Rutgers University, made talk in the I.Gelfand's Seminar Lecture: Schrodinger Operators on Graphs, Symplectic Geometry and Topology April 26-29, USA, Wichita University, Midwest Geometry Conference, made talk Lecture: Poisson Structures and Riemannian Geometry May 23-27, Russia , Moscow State University, I.Petrovski Centenary Conference, Plenary Talk Lecture: Topological Phenomena in Metals June 3-29, Korea, Seoul, KIAS, visiting Distinguished Professor, made 2 lectures Lecture 1: Holomorphic Bundles over Riemann Surfaces and Difference Commuting Operators Lecture 2: Weakly Nonlocal Poisson Structures and Riemannian Geometry July 6-8, Russia, Nizni Novgorod State University, A.Andronov Centenary Conference, made Plenary Talk Lecture: Normal Metals: Topology and Dynamical Systems July 17-20, Russia, St Petersburg, Euler Institute, European Summer School, made lecture Lecture: Geometry of the Weakly Nonlocal Poisson Brackets August 6-25, UK, Cambridge, Newton Institute for Math Sciences, Spring Semester dedicated to the ''Integrability'', made 4 lectures Lectures 1-4: Discrete Integrable Systems August 30, Russia, Moscow Independent University Lecture Lecture: Geometry and Poisson Structures September 21-23, USA, Columbus, Ohio State University, AMS Meeting, Section Talk Lecture: Discrete Spectral Symmetries and Discrete Operators December 15-17, USA, Rutgers University, Conference in honor of M.Fisher, made Plenary Talk Lecture: 3D Normal Metals and Topology December 28-29, Russia, Moscow Independent University, Conference dedicated to the 10th Anniversary of Independent University, Plenary Talk Lecture: Discretization and Integrability 2002: February 28-March 3, USA, Indiana University, Made Colloquium Talk Lecture: 3D Normal Metals and Topology March 27-30, USA, Boston, Northeastern University, Made Talk Lecture: Discrete Systems and Integrability April 10-14, USA, Gainesville, Florida, University of Florida, made Fourth Erdos Colloquium Lecture: Topological Phenomena in Metals June 1-9, Brazil, Rio de Janeiro, IMPA 50th Anniversary Conference, made Plenary Talk Lecture: Fermi Surfaces and Dynamical Systems June 11-15, Italy, Rome University ''La Sapienza'', Conference in honor of Iona-Lasinio, made Plenary Talk Lecture: Topological Phenomena in the Strong Magnetic Field June 17-21, Germany, Dresden, Max Plank Institute, Workshop ''Topology and Physics'', made lecture Lecture: Topological Phenomena in Normal Metals July 19-21, Russia, Dubna, Workshop organized by the Independent University and Center of Permanent Math Education for High School and University Students, made a lecture September 25-October 9, Italy, Trieste, SISSA, Workshop ''Integrable Systems'' made lecture Discrete Completely Integrable Systems October 31-November 30, Korea, Seoul, KIAS, visiting distinguished professor, made 2 lectures Lecture 1: Discretization and Integrability Lecture 2: Topological Charge of the real Sine-Gordon solutions 2003: January 9, Russia, Moscow, Steklov Math Institute, Conference in honor of V.Vladimirov, made Plenary Talk Lecture: New Discretization of Complex Analysis April 7-10, USA, Buffalo NY, University of Buffalo, made 3 Myhills Lectures Lecture 1: Topological Phenomena in Metals Lecture 2: New Discretization of Complex Analysis Lecture 3: Discrete$GL_n$-Connections June 12-17, Moscow State University, A.Kolmogorov Centenary Conference, made Plenary Talk Lecture: Dynamical Systems on Fermi Surfaces, Topology and Conductivity June 25-30, Switzerland, Zurich, Conference ''Topology and Robotics, made talk Lecture: Discrete Connections and Discrete Complex Analysis July 19-20, Russia, Dubna, Conference ''Math for High School and University Students '' (Center for Permanent Education and Independent University), made a lecture Lecture: Discretization and Integrability July 25-29, Russia, St Petersburg, Euler Institute, Conference Discrete Integrable Systems, made talk Lecture: Discretization of$GL_n$Connections and Complex Analysis August 25-27, Russia, Kazan University, Conference ''Geometry and Natural Sciences'', made lecture Lecture: Discrete Differential-Geometrical Connections and Discrete Complex Analysis September 1-3, USA, Boston, Conference ''Unity of Mathematics'' in honor of I.Gelfand's 90th birthday, made Plenary Talk Lecture: Discrete Complex Analysis and Geometry October 1-4, USA, Denver, AMS Meeting, made Section Talk Lecture: Topological Phenomena in Metals November 5-9, Mexico, Juarez, National University of Mexico Colloquium, Center for Advanced Studies Lecture: Discretization and Symmetry 2004: March 25-28, USA, Columbus, Ohio State University, Seminar Talk Lecture: Discretization of Complex Analysis and Connections April 13-15, USA, College Station, TX, Colloquium Talk Lecture: Discretization of Complex Analysis and Connections May 12-15, USA, Sacramento, University of California, Davis, Conference in honor of A.Schwarz, made talk Lecture: Discretization of Complex Analysis and Connections May 31-June 8, Israel, Jerusalem, Conference dedicated to the 250th Anniversary of Moscow State University, made talk Lecture: Discretization of Complex Analysis and Connections June 11-15, Russia, St Petersburg, Euler Institute, Conference in honor of A.Vershik, made talk Lecture: Discretization of Complex Analysis and Connections June 25-July 7, Sweeden, Stockholm, Satellite Conference to the European Math Congress-2004, made invited talk Lecture: Discretization of Complex Analysis and Connections July 19-20, Russia, Dubna, Workshop organized by the Independent University and Center of Permanent Education, made lecture for high school and university students Lecture: Discrete Systems August 18-24, Russia, Moscow, Steklov Institute, Conference dedicated to 100th Anniversary of L.Keldysh, made Plenary Talk Lecture: New Discretization of$GL_n$-Connections and Linear Operators October 6-October 10, Belgium, Brussels, Solvay Conference ''150th Anniversary of H.Poincare', made Plenary Talk Lecture (dedicated to the 150th Anniversary of H.Poincare' and to 100th birthday of H.Cartan): Henry Poincare' and XXth Century Topology October 22-24, USA, Evanston, IL, AMS Meeting, made Section Talk Lecture: Topology of the Quasiperiodic Functions on the Plane December 15-20, Switzerland, Zurich, Conference Topology of the Closed 1-forms, made Invited Plenary Talk Lecture: Topology of the Quasiperiodic Functions on the Plane 2005: March 11-13, USA, Arizona, Tucson, Conference in honor of H.Flashka, made Plenary Talk Lecture: Topological Phenomena in the Theory of Sine-Gordon Equation March 16-17, USA, New York, Columbia University, Conference in honor of Joan Birman ''Low-Dimensional Topology: Knots and Braids'', made Plenary Talk Lecture: Topology of Foliations on Riemann Surfaces given by Real Part of Holomorphic 1-form May 20-26, Israel, Wolf Prize Awarding Ceremony in Jerusalem, Knesset, made 2 lectures in Tel Aviv University and Haifa, Technion Lecture 1: Topological Phenomena in Normal Metals and Quasiperiodic Functions Lecture 2: Riemann Surfaces and Dynamical Systems July 19-21, Russia, Dubna, Workshop organized by Independent University and Center of Permanent Math Education of the High School and University Students, made a lecture September 19-25, Italy, Bressanone/Brixen (Sinai Conference) and Trieste, SISSA; made invited talk in SISSA Lecture: Quasiperiodic Functions and Dynamical Systems November 4-6, USA, Princeton University, Conference in honor of A.Polyakov, made talk Lecture: Topological Phenomena in Normal Metals November 9-12, Mexico, Cocoyoc, III FENOMEC mini-workshop, Selected Topics in Math Physics in honor of A.Perelomov, made 2 lectures Lecture 1: Topological Phenomena in Metals Lecture 2: Riemann Surfaces and Dynamical Systems 2006: March 15-16, USA, Durham NC, University of North Carolina, made Colloquium Talk Lecture: Topology and Quasiperiodic Functions in the Theory of Metals March 19-21, USA, College Park, Math Department, Conference in honor of Ya.Sinai, made talk Lecture: Hamiltonian Foliations of Riemann Surfaces April 7-9, USA, South Bend IN, AMS Meeting, University of Notre-Dame, made talk Lecture: Discrete Systems July 19-20, Russia, Dubna, Workshop organized by Independent University and Center of the Permanent Math Education for the High school and University students, made a lecture September 9-12, USA, Seattle, University of Washington, SIAM Conference in Nonlinear Waves and Coherent Structures, made Section talk Lecture: Discrete Integrable Systems \pagebreak 2007: January 7-20, UK, Cambridge, Newton Institute for Math Sciences, Spring Semester dedicated to discrete systems, made talk Lecture: Discrete Systems and Graphs May 9-May 14, Norway, Bergen, Conference in Complex Analysis, made Plenary Talk Lecture: Discrete Complex Analysis May 28-June 4, UK, Cardiff, Satellite Conference of the Newton Institute, made talk Lecture: Discrete Complex Analysis and Discrete Connections June 10-15, Russia, St Petersburg, Euler Institute, Conference dedicated to L.Euler 250th Anniversary, made talk Lecture: Discrete Complex Analysis and Discrete Geometry July 18-20, Russia, Dubna, Workshop organized by the Independent University and Center for the Peranent Math Education of High School and University Studens, made a lecture August 20-24, Russia, Moscow, Russian Academy of Sciences, Conference in honor of V.Arnold, made talk Lecture: Discrete Integrable Systems and Discrete Complex Analysis November 12-15, USA, Atlanta, Georgia Tech, Distinguished Lectures Series Lecture 1: Analysis on Graphs and Symplectic Geometry Lecture 2: New Discretization of Complex Analysis December 12-22, Russia, Moscow State University, Made Lecture Lecture: Discretization of$GL_n$Connections 2008: March 12-14, USA, Nashville TN, Vanderbilt University, MATH Colloquium Lecture: New Discretization of Complex Analysis June 7-12, USA, University of Maryland, College Park, CSCAMM Conference (Nonlinear Hyperbolic Evolution Equations), made Plenary Talk Lecture: Hamiltonian PDE Systems and Dispersive Shock Wave June 12-19, Canada, Montreal, University of Montreal, Workshop, made 4 lectures under the General Title 4 Lectures: ''Discretization and Complete Integrability'' June 30-July 8, France, Paris-University Paris-VII and University of Nantes, made 2 lecture under the same title in both places: Lectures: ''New Discretization of Complex Analysis'' July 8-13, UK, Manchester University, Adams Room Opening Ceremony and Lecture Lecture: Algebraic Topology and J.F.Adams July 19-21, Russia, Dubna, Workshop organized by Independent University and Center of Permanent Math Education for High School and University Students, made a lecture November 17, USA, Washington DC, Howard University, MATH Colloquium Lecture: New Discretization of Complex Analysis 2009: February 1-March 30, UK, Cambridge, Newton Institute, DIS Program, made a talk Lecture: New Discretization of Complex Analysis May 10-June 10, UK, Cambridge, Newton Institute, DIS Program, made general lecture Lecture: Completely Integrable Systems and Complex Analysis June 12-13, Russia, St Petersburg, Euler Institute, Conference dedicated to the 75th Anniversary of Steklov Institute, made talk Lecture: New Discretization of Complex Analysis June 23-July 1, Israel, Tel Aviv University, Conference in hohor of V.Milman, made Plenary Talk Lecture: New Discretization of Complex Analysis July 12-18, Austria, Vienna, Conference in honor of P.Gruber, made talk Lecture: New Discretization of Complex Analysis Lecture: July 19-20, Russia, Dubna, Workshop of Independent University and Permanent Center of Math Education for High School and University Students, made lecture: Lecture: Graphs, Scattering, Elementary Symplectic Geometry August 2-3, Russia, Chernogolovka, Landau Institute for Theor Physics, Conference in honor of V.Zakharov, made talk (joint with P.Grinevich) Lecture: Singular Finite-Gap Operators and Indefinite Metric October 6, Russia, Moscow, Joint Meeting of Russian Academy of Sciences and Moscow State University dedicated to the 100th Anniversary of N.Bogoliubov, made speech as a recipient of the N.Bogoliubov's Gold Medal-2010 of Russian Academy Laureates Speech: N.Bogoliubov: Physics and Mathematics; Personal impressions. 2010: March 25-26, USA, Tucson, Arizona, Conference "Frontiers of Nonlinear Physics" in honor of V.Zakharov, made talk (with P.Grinevich) Lecture: Singular Solitons and Indefinite Metric May 25-26, Oslo, Norway: Attended Abel Prize Royal Ceremony as a Member of Committee June 7-12, Alghero, Sardinia, Italy, Attended Conference dedicated to B.Dubrovin 60th birthday, made talk ''Purely Magnetic 2D Pauli Operator and Algebraic Geometry'' June 14-July 4, Beijing, China, Attended Confrence '' Nonlinear Waves'' and made talk ''Singular Solitons and Indefinite Metric'', visited Beijing (Tsinghua)University and made 2 lectures anout New Discretization of Complex Analysis in Euclidean and Hyperbolic (Lobatchevski ) Planes. July 6-7, Visited Sofia, Bolgaria, attending meeting of the Council of the European Math Society for the elections of New President and some board members. July 20-25, Dubna, Russia. Made lelementary lecture about Graphs and Symplectic Geometry August 6-16, visited Prague, no talks August 17, made video talk for the Conference ''Nonlinear Waves'' in Pondicherry, India and simultaneously for the Conference in Moscow, Steklov Institute, dedicated to the memory of B.Delauney ''New Discretization of Complex Analysis'' 2011: Worked Spring Semester in Maryland (January 20-May 12) April 10-16: Visited Conference in Brasil, Rio Da Janeiro, dedicated to the 90th birthday of Moricio Peixoto. Made Plenary Talk ''New Discretization of Complex Analysis'' Returned to Moscow on May 13, 2011. Visited relatives in Tashkent , May 20-26 (no talks) May 31: Participated in the Conference at the Moscow State University dedicated to the 110th Anniversary of I.G.Petrovski, made talk ''Supersymmetric 2D Pauli Operator and Algebraic Geometry'' June 4-June 10: Visited Serbia, Belgrade, made series of lectures in the Serbian Academy of Art and Sciences (one lecture in mathematics ''New Discretization of Complex Analysis'' and another one more general for Phys-Math Community) June 10-June 18: Visited Chernogoria (Montenegro), Podgorica and sea resorts, made talks in the Montenegro Academy of Art and Sciences, elected a Honorary Member of this Academy Returned to Moscow at June 18, 2011. At July 8, 2011 returned to USA, Maryland. No trips has been made after that. Recent talks of S.P.Novikov: 1.Speech on the Academy Meeting dedicated to N.Bogoliubov: Ceremony awarding the Bogoliubov Gold Medal, MSU October 6, 2009 2. Joint talk with P.Grinevich at the Conferences dedicated to the 70th birthday of V.Zakharov (Chernogolovka, Russia, August 2, 2009 and Tucson, Arizona, USA, March 26, 2010) Singular Finite-Gap Operators and Indefinite Metric 3.New Discretization of Complex Analysis (Lecture 1, Lecture 2): Many talks including 2 lectures in the Newton Institute, Spring 2009, Invited Plenary talks in several conferences in after 2003 4.Discrete GL(n) Connections and Linear Operators (L.Keldysh 100 Anniversary Conference, Steklov Institute, 2004 and several talks after that 5.Operators on Graphs, Symplectic Geometry and Topology, a number of talks after 1997 6.The Hamiltonian Hydrodinamic type Systems and Dispersive Analog of Shock Waves, Plenary talk at the Conference in Hyperbolic systems, University of Maryland June 12 2008 7.Topological Phenomena in Metals, Invited talk at the Conference dedicated to the 90th birthday of I.Lifshitz, MSU,( Moscow, 1998), Conferences dedicated to the 70th birthdays of M.Fisher (Rutgers 2001), 65th birthdays of Sinai and Ruelle (Rutgers, 2000), 70th birthday of J.Iona-Lasinio (Rome 2002), 50th Anniversary of IMPA (Rio, 2002) and many other talks 8. Henri Poincare and Topology, dedicated to the 150th Anniversary of H.Poincare' and 100th Anniversary of H.Cartan. Invited Plenary Talk at the Solvey Conference ''150th Anniversary of Poincare'', Brussels, October 2004 9. Sardinia, Italy, June 7-12, 2010, Dubrovin 60th Birthday Conference, Talk ''Purely Magnetic 2D Pauli Operator and Solitons'' (joint work with Grinevich and Mironov). Corrected version of the "2D Purely Magnetic Pauli Operators'', Mexico, September 30-October 1, Conference in Math Physics dedicated to 60th birthday of Sasha Turbiner. Mistake for$g=1$is corrected. Additional information concerning the case$g>1\$ is added. New version is presented here as a talk at the Krichever 60th Birthday Conference, December 27-30, Moscow, Russia. The last improved version was presented at the Conference in May 3-7, 2011, Columbia University, New York, USA, dedicated to I.Krichever (click here)