**Novikov, Sergei Petrovich**

Department
of geometry and topology (Head of the Department)

**Office:** 528

**Phone:** (095) 135 14 90

**Email:** __snovikov@mi.ras.ru__, __novikov@ipst.umd.edu__

Principal
fields of research:

Geometry and Topology (Algebraic, Homotopy and Differential Topology, Foliations, Topological Phenomena
in Variational Calculus).
Dynamical Systems.
Mathematical and Theoretical Physics (The Methods of Algebraic, Symplectic, Riemannian Geometry, Topology and
Dynamical Systems in General Relativity,
Completely Integrable Systems and Solitons, 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

Novikov's official CV at the University of Maryland

Full list of Novikov's courses at the University of Maryland for the period 1996--2015

Russian mathematicians in the 20th century. Memoirs. Essays. Public Speeches.

Born:

Father - Petr Sergeevich Novikov (1901-1975),
outstanding mathematician (Descriptive Set Theory, Inverse Problem for the
Newtonian Gravity, Mathematical Logic and Combinatorial Group Theory),

Mother - Keldysh Lyudmila Vsevolodovna (1904-1976),
well-known mathematician, full professor (Set Theory and Geometric Topology).

1955-1960 Study in Moscow State University Department
of Mathematics and Mechanics,

1960 Student diploma from the Department of
Mathematics and Mechanics of MSU.

Thesis title: "Homotopy properties of Thom complexes", (Prof. M. M.
Postnikov -- adviser).

1960-1963 Aspirantura, the Steklov Institute of
Mathematics (Prof. M. M. Postnikov -- adviser).

1964 Candidate of Science (=PhD) in Physics and
Mathematics.

Thesis title: "Differentiable sphere bundles".

1965 Doctor of Science in Physics and Mathematics,

Thesis title: "Homotopy equivalent smooth manifolds".

1962 Married Eleonora Tsoi (Novikova), 3 children, 1 son (Petr) and 2 daughters(Irina and Maria).

1963-1975: The staff at the Steklov Institute of Mathematics,
junior researcher till 1965, senior researcher
after 1965

1965 - The staff at the Department Mathematics and Mechanics
of Moscow State University, Chair of Differential Geometry,
full professor since 1967

1971 - 1993 Head of the Mathematics Group at the L. D. Landau
Institute for Theoretical
Physics of the Academy of Sciences of the USSR,
after 1993--Principal Researcher in the same Institute

1983 - Head of the Chair in Higher Geometry and Topology
of Moscow State University

1984 - Head of the Group in Geometry and Topology of the Steklov
Mathematical Institute
of the Academy of Sciences of the USSR

02/1991-08/1991 Research professor, Laboratory of Theoretical
Physics, Ec. Norm. Sup. de Paris, France

1992-1996, Spring Semesters

University of Maryland at
College Park, visiting professor.

1996- full professor IPST
and Math Department, Distinguished Professor since 1997.

June 2000,
June 2001
and November 2002- Visiting Distinguished Professor of KIAS, (South)
Korean Republic, Seoul.

2009 - February 01 - March 30 and May 10 - June 10, Newtone Institute for Math
Sciences, Cambridge, UK: Invited Prticipant of the Program "Discrete Integrable Systems"

1983--1986 and

2000--2002 Member of Fields Medal Committees of The
International Mathematical Union

(for the International Mathematical Congresses in Berkeley, 1986
and Beigin, 2002)

1985--1996 President of the Moscow Mathematical Society

1986--1990 Vice--President of the International Association of Mathematical Physics

1986-- Editor-in-Chief of the Journal ''Uspekhi Math Nauk'' (=
''Russia Math Surveys'')

1967-1972 Member of Lenin Komsomol Prize Committee for young scientists;
Chairman of the Expert Group in Mathematics, Mechanics and Informatics.

1983-1988 Member of Expert Committee in Mathematics, Mechanics and Informatics
of the Highest Attestation Committee (VAK USSR)

1983-2007 Member of International Lobachevski Prize Committee of USSR/
Russian Academy of Sciences; Chairman after 1991.

1985-1991 Member of Expert Group in Mathematics, Mechanics and Informatics
of Lenin and State Prize Committee of USSR.

1983-2001 Member of Expert Group in Mathematics, Mechanics and Informatics
of State Prize Committee of Russian Federation.

1984--1991 Head of the Geometry/Topology Problem Committee
at the Mathematical Division of the Academy of Sciences of USSR

1994--1996 Member of the Program Committee of the European Math.
Society

(for the 2nd European Math Congress, Budapest, July 1996)

1995--1998 Member of the Program Committee of the International
Mathematical Union

(for the International Mathematical Congress, Berlin, August 1998).

1993--1998 Head of the Expert Committee in Mathematics, Mechanics, Informatics
in the Russian Foundation for the Fundamental Research (RFFR)

2001--2002 Co-chair (with P-L. Lions) of the International Program
Committee for the European Conference in Applied Mathematics/
Applications of Mathematics= AMAM2003
(Nice, 2003)

2006-2007 Member of the Shaw Prize Committee

2008-2010 Member of the Abel Prize Committee

1964- Moscow Math Society Award for young mathematicians

1966-1981 Corresponding member of the

1967 - Lenin Prize

1970 - Fields Medal of the International Mathematical
Union

1981 - Lobachevskii International Prize of the

1981 - Full Member of the

1987 - Honorary Member of the London Math. Society

1988 - Honorary Member of the Serbian Academy of Art
and Sciences

1988 – Doctor Honoris Causa, University of Athens

1991 - Foreign Member, "Academia de Lincei",
Italy

1993- Academia Europea, member

1994 - Foreign associate, National Academy of
Sciences, USA

1996 - Member, Pontifical Academy of Sciences
(Vatican)

1997 - Distinguished University Professor, University
of Maryland at College Park

1998 - Conferences in Honor of 60th birthday:

Solitons, Geometry, Topology: On the Crossroads,

a)Steklov Math Institute and Landau Institute for
Theor Physics, Moscow, Russia, May 26-31, 1998

b)University of Maryland at College Park, College
Park, MD, September 24-26, 1998.

1999 - Doctor Honoris Causa,

2003 – Fellow,

2005 - Wolf Prize in Mathematics

2008 - Pogorelov Prize of the Ukranian National Academy of Sciences (NANU)

2009 - Bogoliubov Gold Medal of the Russian Academy of Sciences and Dubna Institute
for the Nuclear Research

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''

Over 30 Novikov's students became PhD. Part of them got the scientific degree
''Doctor of Physico-Mathematical Sciences'' (the second doctor degree
equivalent to the scientific level of full professor):

V.Golo, V.Buchstaber**, A.Mishchenko**, G.Kasparov**,
O.Bogoyavlenski**, F.Bogomolov**, S.Gusein-Sade, I.Krichever**,**,
B.Dubrovin**,**, I.Taimanov, A.Veselov*, I.Babenko, R.Nadiradze, V.Vedenyapin, M.Brodski,
S.Tsarev, O.Mokhov, R.Novikov, P.Grinevich, I.Dynnikov*, A.Maltsev.

Other former students of S. Novikov who received the
PhD level or the scientific degree ''Candidate of Physico-Mathematical
Sciences'' (which is a Soviet/Russian equivalent of PhD) are the following:

A.Brakhman, V.Peresetski, A.Grigoryan, Th.Voronov,
A.Zorich, N.Panov, A.Lyskova, M.Pavlov, Le Tu Thang, L.Alania, D.Millionshikov,
S.Piounikhin, V.Sadov, A.Lazarev, R.Deleo, A.Giacobbe, K.Kaipa.

People whose names are marked by ** were invited
speakers of the International Math Congresses or the plenary speakers of the
European Math Congresses and/or International Congresses in Math Physics, the
names marked by * were invited section speakers of the European Math
Congresses.

Topology

**
Differentiable Manifolds and Characteristic Classes**

Topological Invariance of Rational Pontryagin Classes
(1965).

Homotopy Invariance of the special
Pontryagin-Hirzebruch Integrals along the cycles coming from the Homological
Algebra of fundamental group (1965-70). The Higher Signature Conjecture -
''Novikov Conjecture'' (1970). Hermitian Analog of the Algebraic K-Theory for
the rings with involution and Symplectic Algebra (1970).

Classification of the closed simply connected
manifolds (*n>4* ) of the same tangential homotopy type.
Browder-Novikov theory. There is only a finite number of manifolds with the
same Rational Pontryagin Classes (1961-64).

The Recognition Problem of the *n*-sphere is
undecidable for *n>4* (1962, published later): it was included in the article of I.Volodin,
V.Kuznetsov and A.Fomenko as the section **10. A theorem of S.P.Novikov**

**
Study of Multiplicative Structure in the Rings of Stable Homotopy Groups of Spheres
and Cobordisms**

First proof of existence of arbitrary long nontrivial superpositions in the Stable Homotopy Ring
for Spheres (1959):calculation of multiplication in the most important old and new cobordismrings:
Real Orientable and Unitary --- see footnote to the item n 6 of publications about the priority
relations here; Special Unitary and Symplectic. These results are based on the developement of
algebraic and geometric technique associated with Adams
Spectral Sequence. In particular, cohomology of Hopf Coalgebras and new type ''Steenrod-like''
Operations in cohomology of Hopf
Algebras over the finite fields play fundamental role here(1959-62).
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 *C*^{1}-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 *C ^{n}*. 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).

**
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.,

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 (4*k*+2)-dimensional manifolds. Dokl. Akad. Nauk
SSSR, 1963, v. 153, N 5, 1005-1008 (submitted 13.06.1963).

9. Differential topology, Itogi Nauki (Algebra and Topology), Inst. Nauchn.
Informatsii Akad. Nauk SSSR, 1963, 134-160.

10. Homotopically equivalent smooth manifolds, I. Izv.
Akad. Nauk SSSR, 1964, v 28, N 2, 365-474.

11. Foliations of codimension 1 on manifolds, Dokl. Akad. Nauk SSSR, 1964, v.
155, N 5, 1010-1013.

12. Foliations of codimension 1, Dokl. Akad. Nauk SSSR, 1964, v. 157, N 4,
788-790.

13. Smooth foliations on three-dimensional manifolds, Uspekhi Mat. Nauk, 1964,
v. 19, N 6, 89-91.

14.

15. Gorki mathematical seminar on homotopic topology (June 1964), Uspekhi Mat.
Nauk, 1964, v. 19, N 6, 237-238 (with M. I. Vishik and M. M. Postnikov).

16. The Topology Summer Institute, Seattle, 1963, Uspekhi Mat. Nauk, 1965, v.
20, N 1, 147-170.

17. New ideas in algebraic topology (K-theory and its applications). Uspekhi
Mat. Nauk, 1965, v. 20, N 3, 41-66.

18. Homotopic and topological invariance of certain rational classes of
Pontryagin. Dokl. Akad. Nauk SSSR, 1965, v. 162, N 6, 1248-1251.

19. Topological invariance of rational Pontryagin classes. Dokl. Akad. Nauk
SSSR, 1965, v. 163, N2, 298-300.

20. Differentiable sphere bundles, Izv. Akad. Nauk SSSR,
1965, v. 29, N 1, 71-96.

21. Rational Pontryagin classes, Homeomorphism and homotopy
type of closed

22. Structures on manifolds, Proc. 4th All-Union Topology Conference (

23. The topology of foliations, Trudy Moskov. Mat. Obshch,
1965, v. 14, 248-278.

24. On manifolds with free Abelian fundamental group and their 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

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.

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32. Adams operators and fixed points. Izv. Akad. Nauk
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34. Pontryagin classes, the fundamental group and some problems of stable
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35. Algebraic construction and properties of Hermitian analogues of K-theory
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36. Algebraic construction and properties of Hermitian analogues of K-theory
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38. Formal groups, power systems, and Adams operators.
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39. Formal groups and their role in the apparatus of algebraic
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40. On some characteristics of cosmological models, Zh. Eksper. Teoret. Fiz.,
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42. Singularities of the cosmological model of the Bianchi IX type according to
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45. A periodic problem for the Korteweg-de Vries and Sturm-Liouville equations.
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46. Qualitative theory of homogeneous cosmological models, Trudy Sem.
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47. The connection between the Hamiltonian formalisms of stationary and
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48. Non-linear equations of Korteweg-de
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49. The Schroedinger equation in a periodic field and Riemann surfaces, Dokl.
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50. Homogeneous models in general relativity theory
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51. Algebraic topology, Encyclopedia of Mathematics, 1977, vol. 1, 170-174.

52. Petr Konstantinovich Rashevskii (on his seventieth Birthday), Uspekhi Mat.
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53. Methods of algebraic geometry in contemporary mathematical physics, Math.
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54. Problems in geometry,

55. Holomorphic vector bundles over Riemann surfaces and the
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56. A method of solving the periodic problem for the Korteweg-de Vries equation
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57. Algebraic geometry and mathematical physics, Proc. Conf. on fundamental
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58. Modern geometry. Methods and applications, Nauka,

59. Holomorphic fiberings and non-linear equations. Finite zone solutions of
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60. Solutions to the Ginzburg-Landau equations for planar textures in
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61. Methods of qualitative theory of dynamics systems in general relativity
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62. Holomorphic bundles over algebraic
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63. The theory of solitons and method of the inverse problem, Nauka,

64. Ground states of a two-dimensional electron in a periodic magnetic
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65. Ground states in a periodic field. Magnetic Bloch functions and vector
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66. A method of solving the periodic problem for the KdV equations and its
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67. Linear operators and integrable Hamiltonian systems, Proc. Intern. Congr.
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68. Multivalued functions and functionals. An analogue of the Morse theory,
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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,
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70. Variational methods and periodic solutions of equations of Kirchhoff type.
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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,
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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.
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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
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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.
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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.
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79. Topological and algebraic-geometrical methods in contemporary mathematical
physics, Soviet Scientific Reviews, 1982, v. 3, 1-156 (with B. A. Dubrovin and
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80. Hamiltonian formalism of one-dimensional systems of hydrodynamic type and
the Bogolyubov-Whitham averaging method, Dokl. Akad. Nauk SSSR, 1983, v. 270, N
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81. Two-dimensional Schroedinger operators in periodic fields. Current Problem
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82. Multivalued functionals in modern mathematical physics, Atti Accad. Sci.
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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.
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85. Poisson brackets and complex tori. Trudy Mat. Inst. Steklov, 1984, v. 165,
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86. Modern geometry. Methods of homology theory, Nauka, Moscow 1984 (with B. A.
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87. Periodic extremals of many-valued or not everywhere positive functionals,
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88. On Poisson brackets of hydrodynamic type, Dokl. Akad. Nauk SSSR, 1984, v.
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89. Discussion with Academician S. P. Novikov, Kvant, 1984, N 10, 2-5.

90. Finite-zone two-dimensional potential Schroedinger operators. Explicit
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91. Finite-zone two-dimensional Schroedinger operators. Potential operators,
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92. Algebro-topological approach to reality problems Real action variables in
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93. An averaging method for one-dimensional systems, in Non-linear and
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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
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97. Analytical homotopy theory. Rigidity of homotopic integrals, Dokl. Akad.
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98. Integrable systems, I. Current problem in mathematics. Fundamental
directions. VINITI, 1985, v. 4, 179-284 (with B. A. Dubrovin and

99. Two-dimensional periodic Schroedinger operators and Prym's q-functions, in Geometry Today, Internat. Conf. Rome, June 1984,

100. Differential geometry and the averaging method for field-theoretic
systems, Proc. III Internat. Symp. on Selected Problem in Statistical Mechanics
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101. Modern geometry. Methods and applications. 2nd revised edition, Nauka,

102. Bloch homology. Critical points of functions and closed I-forms, Dokl.
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103. Morse inequalities and von Neumann 1-factors, Dokl. Akad. Nauk SSSR, 1986,
v. 289, N 2, 289-292 (with M.Shubin).

Morse inequality and von Neumann algebras, Proc. I. G. Petrovskii seminar, Russian Math. Uspehi 41:4(250)
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Morse theory and von Neumann invariants
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104. Topology I. Current problem in mathematics. Fundamental directions,
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105. Two-dimensional Schroedinger operators: Inverse
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106. Vladimir Abramovich Rokhlin (obituary), Uspekhi Mat. Nauk, 1986, v. 41, N
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107. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad.
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108. Elements of differential geometry and topology, Nauk,

109. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad.
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110. Algebras of Virasoro type, Riemann surfaces and
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111. Virasoro-type algebras, Riemann surfaces and strings in
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112. Two-dimensional Schroedinger operator and solitons: 3-dimensional
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113. The two-dimensional inverse scattering problem for negative
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114. Analytical theory of homotopy groups, in Topology and Geometry, Rochlin
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115. Algebras of Virasoro type, energy-momentum tensor and
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116. Hydrodynamics of the soliton lattices. Differential
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117. Riemann surfaces, operator fields, strings. Analogues of the
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118. On the quantization of finite-zoned potentials in connection with string
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119. On the equation [*L,A*] =\eps{\cdot}1, Progress of Theor Physics,
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120. Riemann Surfaces, Operator Fields, Strings. Analogues of the
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121. Hydrodynamics of the Soliton Lattices and Differential Geometry.
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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.
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123. Action-angle Variables and Algebraic Geometry, in the volume La
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124. Integrability in Mathematics and Theoretical Physics: Solitons. The
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125. Role of Integrable Models in the development of Mathematics. (Mathematical
Research today and tomorrow: Viewpoints of seven Fields Medallists). LNM,
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126. Quasiperiodic structures in Topology, In: Topological Methods in
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127. On the Liouville form of the Poisson bracket of Hydrodynamic type and
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128. Hydrodynamics of Soliton Lattices. Mathematical Physics Reviews, ed by B.
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129. String Equation - 2. Physical Solution, Algebra and Analysis, 1994, v. 6,
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130. Solitons
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131. The Semiclassical Electron in a Magnetic Field and Lattice. Some Problems
of the Low Dimensional Periodic Topology, Geometric and Functional
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132. Nonselfinersecting magnetic orbits on the plane. Proof of Principle of the
Overthrowing of the Cycles, Topics in Topology and Mathematical Physics, 1995,
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133. Exactly solvable periodic 2-d Schroedinger operators.
Russian Math.Surveys, 1995, v 50, n. 6, pp 171-172
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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.
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138. Laplace Transformations and Simplicial Connections.
Russian Math Surveys, 1997, v 52, n 6, pp 157-158
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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 -
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Buchstaber and S. Novikov, (with A. P. Veselov) Appendix I (S. Novikov):
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141. Role of Integrable Models in the development of Mathematics In: ''Fields
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142. Topological Phenomena in Normal Metals, Uspekhi Phys. Nauk, March 1998, v
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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.
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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
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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
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157. A note on the real fermionic and bosonic quadratic forms: diagonalization and
topological interpretation, arXiv,
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158. On the exotic de-Rham cohomology. Perturbation
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159. Geometry of the triangle equation on two-manifolds. Moscow Mathematical Journal, v 3(2003), pp 419-438
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160.Topological Phenomena in the Real Periodic Sine-Gordon Theory, Journal of
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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
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162. 2-dimensional Toda lattice,
commuting difference operators and holomorphic vector bundles, Uspekhi Math.
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163. Discrete Connections on the
Triangulated Manifolds and Difference Linear Equations arXiv, math-ph/0303035. This work
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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)
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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,
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166. Algebraic Topology. Modern Problems of Mathematics.
(Steklov Math Institute Series, founded in 2003),pp 1-46 (in Russian)
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167. On the metric independent exotic homology, preprint,
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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
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169. Topology of foliations given by the real parts of holomorphic 1-forms.
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(v1 - 21 Jan 2005, revised - February, 10, 2005 and March 31, 2005).

170. Topology of the Generic Hamiltonian Foliations on the Riemann Surface.
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171. Dynamical Systems and Differential Forms. Low Dimensional Hamiltonian Systems.
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172. S.Novikov, I.Taimanov. Modern Geometric Structures
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173. New discretization of complex analysis. The Euclidean and hyperbolic planes.
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174. Four Lectures: Discretization and Integrability. Discrete
Spectral Symmetries. Newton Institute for Math Sciences, Cambridge
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175. Four Lectures on Discrete Systems ( Summer School on Integrability of Difference Equations at Montreal, June 2008)
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176. Singular finite-gap operators and indefinite metrics. I.
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(March 2009, with P.Grinevich). Russian Math Surveys==Uspekhi Math 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.
Revised form of this article is published in the Journal Russian Math. Surveys (2015 v. 70:2, pp. 299-329; doi:10.1070/RM2015v070n02ABEH004948 (in english).

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). Published in the Journal ''Bulletin of Brazilian Math Society, New Series, December 2013, 44(4), 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). Published in the Journal ''Russian Math Surveys=Uspekhi Math nauk, 2013, vol 68 n 6.
The article in arXiv does not contain the last '' Appendix 3, Symplectic properties of the real self-adjoint operators on the graphs'' of the article published in RMS, 2013, see also
Russian version of this article

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

188. Spectral Meromorphic Operators and Nonlinear Systems, arXiv math.FA 1409.6349, to appear in the Russian Math Surveys=Uspekhi Math Nauk, 2014, vol 69 n 5 (with P.G.Grinevich)

189. ''Differential Forms'', course MATH437, S.Novikov, University of
Maryland, Spring 2015

190. On the s-meromorphic OD operators, arXiv math. 1510.06770 (with P.G.Grinevich)

**Additional items:**

a) $ 10. A theorem of S.P.Novikov. Included in the article:
I.Volodin, V.Kuznetsov, A.Fomenko. The problem of discriminating algorithmically
the standard three-dimensional sphere. Russian Mathematical Surveys, 1974, v. 29, no. 5,
p. 169-171.

b) "Novikov-Veselov's Quasicrystallographic Groups". Included in the article: Le Tu Thang, S.Piunikhin, V.Sadov. The Geometry of Quasi-Cristals
Russian Math. Surveys (1993), vol. 48, n 1, pp 37-100 - see page 46 (in Russian).

c) The Morse Theory and von Neumann invariants of non-simply-connected
manifolds (in Russian);

The Morse Theory and von Neumann invariants of non-simply-connected
manifolds (translation from Russian with the present authors comments),

Uspekhi Math Nauk=Russian Math Surveys, 1986, vol. 41, n 5, pp.
222-223 (in Russian), Section of Mathematical Life in USSR: Meetings of the
I.G.Petrovski Seminar in Differential Equations and Mathematical Physics,
March 5 1986, 1st meeting, (with M.Shubin)

191. Giroscopes and magnetic orbits Uspekhi Matematicheskih Nauk, 2020

**
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.

**
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.

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)

10. Beijing, China, June 26-29, 2010, Conference ''Nonlinear Waves...'', Plenary Talk ''Singular Solitons and Indefinite Metric'' (joint work with Grinevich)

11. India, Pondicherry, August 17, 2010, Simposium in Nonlinear Waves ( Video Talk) and Moscow, Russia, Steklov Inst., August 17, Delauney Memorial Conference in Geometry, Topology and Combinatorics, Talk ''New Discretization of Complex Analysis'': the introduction and the main body

12.Discrete Triangular Systems. This is a recent talk at the Gelfand Conference in Praesidium, July 2013, Moscow.

13.Singular Solitons and Indefinite Metric. This is a recent talk at the Gelfand Conference in MSU, December 2013

14.Singular Solitons and Spectral Theory.. This is a recent Plenary Talk at the International Conference, August 2014, Moscow, University of Peoples Friendship.