# Sergei Novikov (mathematician)

Sergei Petrovich Novikov | |
---|---|

Born | Gorky, Russian SFSR, Soviet Union |
20 March 1938

Fields | Mathematics |

Alma mater | Moscow State University |

Doctoral advisor | Mikhail Postnikov |

Doctoral students | Ivan K. Babenko Victor Buchstaber Boris Dubrovin Sabir Gusein-Zade de Igor Krichever Iskander Taimanov Anton Zorich |

Notable awards | Lenin Prize (1967) Fields Medal (1970) Lobachevsky Medal (1981) Wolf Prize (2005) |

**Sergei Petrovich Novikov** (also **Serguei**) (Russian: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal.

## Contents

## Early life

Novikov was born in Gorky, Soviet Union (now Nizhny Novgorod, Russia).

He grew up in a family of talented mathematicians. His father was Pyotr Sergeyevich Novikov, who gave the negative solution of the word problem for groups. His mother Lyudmila Vsevolodovna Keldysh and maternal uncle Mstislav Vsevolodovich Keldysh were also important mathematicians.

In 1955 Novikov entered Moscow State University (graduating in 1960). Four years later he received the Moscow Mathematical Society Award for young mathematicians. In the same year he defended a dissertation for the *Candidate of Science in Physics and Mathematics* degree at the Moscow State University (it is equivalent to the PhD). In 1965 he defended a dissertation for the *Doctor of Science in Physics and Mathematics* degree there. In 1966 he became a Corresponding member of the USSR Academy of Sciences.

## Research in topology

Novikov's early work was in cobordism theory, in relative isolation. Among other advances he showed how the Adams spectral sequence, a powerful tool for proceeding from homology theory to the calculation of homotopy groups, could be adapted to the new (at that time) cohomology theory typified by cobordism and K-theory. This required the development of the idea of cohomology operations in the general setting, since the basis of the spectral sequence is the initial data of Ext functors taken with respect to a ring of such operations, generalising the Steenrod algebra. The resulting Adams–Novikov spectral sequence is now a basic tool in stable homotopy theory.

Novikov also carried out important research in geometric topology, being one of the pioneers with William Browder, Dennis Sullivan and Terry Wall of the surgery theory method for classifying high-dimensional manifolds. He proved the topological invariance of the rational Pontryagin classes, and posed the Novikov conjecture. This work was recognised by the award in 1970 of the Fields Medal. He was not allowed to travel to Nice to accept his medal. He received it in 1971 when the International Mathematical Union met in Moscow. From about 1971 he moved to work in the field of isospectral flows, with connections to the theory of theta functions. Novikov's conjecture about the Riemann-Schottky problem (characterizing principally polarized abelian varieties that are the Jacobian of some algebraic curve) stated, essentially, that this was the case if and only if the corresponding theta function provided a solution to the Kadomtsev–Petviashvili equation of soliton theory. This was proved by Shiota (1986),^{[1]} following earlier work by Arbarello and de Concini (1984),^{[2]} and by Mulase (1984).^{[3]}

## Later career

Since 1971 Novikov has worked at the Landau Institute for Theoretical Physics of the USSR Academy of Sciences. In 1981 he was elected a Full Member of the USSR Academy of Sciences (Russian Academy of Sciences since 1991). In 1982 Novikov was also appointed the *Head of the Chair in Higher Geometry and Topology* at the Moscow State University.

In 1984 he was elected as a member of Serbian Academy of Sciences and Arts.

As of 2004^{[update]}, Novikov is the Head of the Department of geometry and topology at the Steklov Mathematical Institute. He is also a Distinguished University Professor at University of Maryland, College Park and is a Principal Researcher of the Landau Institute for Theoretical Physics in Moscow.

In 2005 Novikov was awarded the Wolf Prize for his contributions to algebraic topology, differential topology and to mathematical physics. He is one of just eleven mathematicians who received both the Fields Medal and the Wolf Prize.

## See also

## References

- ↑ Shiota, Takahiro (1986). "Characterization of Jacobian varieties in terms of soliton equations".
*Inventiones Mathematicae*.**83**(2): 333–382. doi:10.1007/BF01388967.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ Arbarello, E.; De Concini, C. (1984). "On a set of equations characterizing Riemann matrices".
*Annals of Mathematics*.**120**(1): 119–140. doi:10.2307/2007073. JSTOR 2007073.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ Mulase, M. (1984). "Cohomological structure in soliton equations and Jacobian varieties".
*Journal of Differential Geometry*.**19**(2): 403–430. MR 0755232.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>

## External links

- Homepage and Curriculum Vitae on the website of Steklov Mathematical Institute
- Biography (in Russian) on the website of Moscow State University
- O'Connor, John J.; Robertson, Edmund F., "Sergei Novikov (mathematician)",
*MacTutor History of Mathematics archive*, University of St Andrews<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>. - Sergei Novikov at the Mathematics Genealogy Project

- BLP articles lacking sources from February 2013
- Interlanguage link template link number
- 1938 births
- Members of the United States National Academy of Sciences
- Fields Medalists
- Living people
- 20th-century mathematicians
- 21st-century mathematicians
- Full Members of the USSR Academy of Sciences
- Full Members of the Russian Academy of Sciences
- Members of the Serbian Academy of Sciences and Arts
- Moscow State University alumni
- Moscow State University faculty
- Russian mathematicians
- Soviet mathematicians
- Topologists
- University of Maryland, College Park faculty
- Wolf Prize in Mathematics laureates
- Lenin Prize winners