# Sergei Novikov (mathematician)

Sergei Petrovich Novikov (Russian: Сергей Петрович Новиков; Sergei Novikov also; born March 20, 1938 in Gorky ) is a Russian mathematician who works in algebraic topology, and mathematical physics. He was awarded the Fields Medal in 1970.

## Life and work

Novikov's father was the mathematician Pyotr Sergeyevich Novikov, who solved the word problem for groups and important contributions to the Burnside problem returned. His mother Lyudmila Keldysh Mstislav Keldysh and his uncle were also mathematicians. Novikov studied from 1955 at the Lomonosov University of Moscow, with a degree 1960 ( Thesis: Homotopieeigenschaften of Thom complexes ). In 1964 he was awarded the prize for young mathematicians of the Moscow Mathematical Society and was founded in 1964 at Postnikov PhD (Candidate title, Differentiable sphere bundle). In 1965 he completed his habilitation (Russian doctorate ) work with homotopy equivalent smooth manifolds. In 1966 he became a corresponding member of the Academy of Sciences of the USSR ( 1981, he became a full member). He was from 1963 to 1975 at the Steklov Institute, since 1965 as a senior scientist. Since 1965 he was also on Mekh -Mat, the Department of Mathematics and Mechanics of Moscow State University, since 1967 a full professorship ( first for differential geometry, from 1983 Higher Geometry and topology). 1971 to 1993 he headed the mathematics group of the Landau Institute of the Russian Academy of Sciences and was then a senior scientist there. From 1983, he led the group Geometry and Topology at the Steklov Institute. He has been a visiting professor at the Ecole Normale Superieure (1991 ), the University of Maryland at College Park (1992 to 1996 in the spring semester, he is since 1997 there Distinguished University Professor ) at KIAS in Seoul (2000 to 2002) and on Isaac Newton Institute ( 2009).

He is since 1962 married to Eleonora Tsoi and has a son and two daughters.

In the 1960s he worked on algebraic topology. Among other things, he showed how homological methods ( spectral sequences of Adams type) and cohomological operators could be applied in the calculation of homotopy groups and in the then new Kobordismen and K- theory. The Adams - Novikov spectral sequences, are an important tool in stable homotopy theory.

He was also with William Browder, Dennis Sullivan and Terry Wall, a pioneer of surgery theory ( Surgery, fragmentation methods used for the classification of higher-dimensional topological manifolds ) in the geometric topology. He proved that rational Pontryagin classes are topological invariants. The Novikov conjecture is a known open question in the topology.

From the 1970s he was principally concerned with mathematical physics ( theory of solitons, integrable systems, etc.) and even moved in 1971 to the Landau Institute for Theoretical Physics. According to him, and AP Veselov Novikov - Veselov equation, the (1984 ) is named, the two-dimensional solitons describes (such as the KP equation).

In 1970 he was awarded the Fields Medal for his work in algebraic topology. He was also awarded the 1967 Lenin Prize, 1981, the Lobachevsky Medal, 2008 Pogorelov price of the Ukrainian Academy of Sciences, 2009, Bogolyubov Gold Medal of the Russian Academy of Sciences and the 2005 Wolf Prize. In 1978 he gave a plenary lecture at the ICM in Helsinki (Linear Operators and Integrable Hamiltonian Systems), was 1966 Invited Speaker at the ICM in Moscow ( Pontrjagin classes, the fundamental group and some problems of the stable algebra ), 1962 in Stockholm (Smooth manifolds of common homotopy type) and 1970 on the ICM in Nice ( Analogues hermitiens de la K- theory ), the Congress could, however, not even visit because he had no permission to travel because of the support of dissidents. He also held in 1977, 1981, 1986 and 1988, plenary lectures on the International Congresses of Mathematical Physics. He is a corresponding full and since 1981 member of the Soviet Academy of Sciences since 1966. Since 1987 he is honorary member of the London Mathematical Society, and since 1988 the Serbian Academy of Sciences. In 1988 he became an honorary doctorate from the University of Athens and in 1999 the University of Tel Aviv. He is since 1991 member of the Accademia dei Lincei, since 1993 the Academia Europaea since 1996, the Pontifical Academy of Sciences, since 2003 Member of the European Academy of Sciences and since 1994, the National Academy of Sciences. 1985 to 1996 he was president of the Moscow Mathematical Society.

His doctoral include Boris Dubrovin Anatoljevich and Igor Krichever.

## Writings

- Basic elements of differential geometry and topology, Dordrecht, Kluwer 1990
- Theory of solitons -the inverse scattering method, New York, 1984
- With Boris Dubrovin, Fomenko Modern geometry- methods and applications, Vol.1 -3, Springer, Graduate Texts in Mathematics ( first in 1984, 1988, 1990, Vol.1 The geometry of surfaces and transformation groups, Vol.2 The geometry and topology of manifolds, Bd.3 Introduction to homology theory, be treated including calculus of variations, crystallographic groups)
- Topics in Topology and mathematical physics, AMS (American Mathematical Society ) 1995
- Integrable systems - selected papers, Cambridge University Press, 1981 ( London Math.Society Lecture Notes )
- With Taimanov Cobordisms and Their application, in 2007, world scientific
- Vladimir Arnold, he is the editor and co-author of the series Dynamical systems Encyclopedia of mathematical sciences, Springer
- Topology - general survey, Bd.1 the topology of the series Encyclopedia of mathematical sciences, Springer 1996
- Solitons and geometry, Cambridge 1994
- Viktor M. Staber book soliton geometry and topology -on the crossroads, AMS
- With Dubrovin, Krichever Topological and Algebraic Geometry Methods in contemporary mathematical physics Vol.2, Cambridge ( Russian Edition Review article )
- My generation in mathematics, Russian Mathematical Surveys Bd.49, 1994, p.1