World Library  
Flag as Inappropriate
Email this Article

Sergei Novikov (mathematician)

Article Id: WHEBN0000628515
Reproduction Date:

Title: Sergei Novikov (mathematician)  
Author: World Heritage Encyclopedia
Language: English
Subject: Fields Medal, Wolf Prize in Mathematics, Graduate Texts in Mathematics, Motion (geometry), List of Moscow State University people
Collection: 1938 Births, 20Th-Century Mathematicians, 21St-Century Mathematicians, Fields Medalists, Full Members of the Russian Academy of Sciences, Full Members of the Ussr Academy of Sciences, Lenin Prize Winners, Living People, Members of the Serbian Academy of Sciences and Arts, Members of the United States National Academy of Sciences, Moscow State University Alumni, Moscow State University Faculty, Russian Mathematicians, Soviet Mathematicians, Topologists, University of Maryland, College Park Faculty, Wolf Prize in Mathematics Laureates
Publisher: World Heritage Encyclopedia

Sergei Novikov (mathematician)

Sergei Petrovich Novikov
Born (1938-03-20) 20 March 1938
Gorky, Russian SFSR, Soviet Union
Fields Mathematics
Alma mater Moscow State University
Doctoral advisor Mikhail Postnikov
Doctoral students Ivan K. Babenko
Victor Buchstaber
Boris Dubrovin
Sabir Gusein-Zade
Gennadi Kasparov
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.


  • Early life 1
  • Research in topology 2
  • Later career 3
  • See also 4
  • References 5
  • External links 6

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 Ludmila 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, 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


  1. ^ Shiota, Takahiro (1986). "Characterization of Jacobian varieties in terms of soliton equations".  
  2. ^ Arbarello, E.; De Concini, C. (1984). "On a set of equations characterizing Riemann matrices".  
  3. ^ Mulase, M. (1984). "Cohomological structure in soliton equations and Jacobian varieties".  

External links

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.