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Principalfields 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 andEducation
Employment
SpecialService
Awardsand Honors
SelectedHonorable Invited Talks
TheScientific School
ScientificResults
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.
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 2001and 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"
1978 Plenary Speaker of the International Mathematical Congress, Helsinki(Theory of Solitons and Algebraic Geometry)
1966 Invited Speaker of the International MathematicalCongress, Moscow, Section of Topology (Presented to the Congress preprint ofthe lecture ''Pontryagin Classes, the Fundamental Group and Some Problems ofthe Stable Algebra'' - later published in the special edition dedicated to 70thbirthday of Georges de Rham; actually made talk in the Cobordism Theory)
1970 Invited Speaker of the International MathematicalCongress, Nice, Section of Topology (''Hermitian Analog of the K-theory andHamiltonian Formalism''; has not been permitted to attend Congress personallyas a punishment for the letters supporting dissidents; the lecture has beenread by other person and published in the Materials of the Congress).
1977, 1981, 1986, 1988 Invited Plenary Speaker of theInternational Congresses in Mathematical Physics in Rome, W.Berlin, Marceilleand 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 SpectralSymmetries'', ''Operators on Graphs and Symplectis Geometry'', ''Topological Phenomena in Normal Metals''
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 AdamsSpectral Sequence. In particular, cohomology of Hopf Coalgebras and new type ''Steenrod-like'' Operations in cohomology of HopfAlgebras 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 ofComplex Cobordism Theory, the Adams-Novikov Spectral Sequence. Complete calculation ofthe ''Steenrod'' algebra of operations as the Operator(Heisenberg) double over the Landveber-Novikov Hopf algebra with specificZ-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 FormalGroups 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 HirzebruchMultiplicative Series through the Formal Group (1966-1971). Further development of algebraic structuresassociated with unitary cobordisms, the fixpoint equations, 2-valued formal group (Buchstaber-Novikov, 1971)
Nonsingular Foliations
Qualitative Theory of The Nonsingular Codimension OneFoliations, especially on 3-manifolds. Existence of Compact Leavefor any nonsingular 2-foliation on 3-sphere and many other 3-manifolds,classification of all topological types ofanalytical foliations in the solid torus based on the conjugacy classes of braids(1963-65). Resent results: Topology of thegeneric foliations on Riemann Surfaces generated by the real partsof holomorphic one-forms. Transversal Canonical Bases andFundamental Semigroup of positive closed transversal curves, itscalculation 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 Morsesingularities. The Quasiperiodic manifolds. Novikov Conjectures concerning thestructure of leaves and analytical properties of the Morse-Novikov Complexgenerated by the closed 1-form and C1-generic Riemannian metric (1981-1991).
Morse Theory for the non-simply-connected manifolds.Morse inequalities and representations of fundamental group, the jumpingsubvarieties for homology groups on the representation space (the analogs ofAlexander Polinomials). Complete calculation of the generic Betti number and all Milnor-FarberSpectral Sequence for one-dimensional representations through the MasseyOperations (1986). Von Neumann factors and Morse inequalities, the Novikov-Shubininvariants of the Laplace-Beltrami Operators on universal covering. The Von Neumannanalog of the Reidemeister-Ray-Singer Torsion. Analog of Morse-Witteninequalitis for smooth real vector fields and diagonalization of real fermionicquadratic 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 ofmappings of spheres in the manifolds, the AnalyticalHomotopy Theory, Module Spaces in The Rational (Real) Homotopy Theory (1984-88).