Sergei Petrovich Novikov (mathematician)

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Sergei Petrowitsch Novikow ( Russian Сергей Петрович Новиков ; also Sergei Novikov ; born March 20, 1938 in Gorki ) is a Russian mathematician who works in algebraic topology and mathematical physics . He received the Fields Medal in 1970 .

Life

Novikov's father was the mathematician Pyotr Sergejewitsch Novikow , who solved the word problem for groups and made important contributions to the Burnside problem . His mother Lyudmila Keldysch and his uncle Mstislaw Keldysch were also mathematicians. Novikow studied from 1955 at the Lomonossow University of Moscow , with a degree in 1960 (diploma thesis: Homotopy properties of Thom complexes ). He had contacts with Vladimir Arnold (whom he introduced to topology) and attended Israel Gelfand's seminar . In 1964 he received the prize for young mathematicians of the Moscow Mathematical Society and received his doctorate in 1964 with Postnikow (candidate title, differentiable spheres bundle ). In 1965 he completed his habilitation (Russian doctorate) with the work Homotopy-Equivalent Smooth Manifolds . In 1966 he became a corresponding member of the Academy of Sciences of the USSR (in 1981 he became a full member). From 1963 to 1975 he was at the Steklow Institute , since 1965 as a senior scientist. Since 1965 he was also at the Mekh-Mat, the department of mathematics and mechanics at Lomonossow University, since 1967 with a full professorship (first for differential geometry, from 1983 higher geometry and topology). From 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 headed the Geometry and Topology group at the Steklow Institute. Among other things, he was visiting professor at the École normal supérieure (1991), the University of Maryland in College Park (1992 to 1996 in the spring semesters, since 1997 he has been Distinguished University Professor there), at the KIAS in Seoul (2000 to 2002) and on Isaac Newton Institute (2009).

He has been married to Eleonora Tsoi since 1962 and has one son and two daughters.

Boris Anatoljewitsch Dubrowin and Igor Krichever are among his doctoral students .

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

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

Honors and memberships

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

In 1970 he received the Fields Medal for his work in algebraic topology . In addition, he received the Lenin Prize in 1967 , the Lobachevsky Medal in 1981 , the Pogorelov Prize of the Ukrainian Academy of Sciences in 2008, the Bogolyubov Gold Medal of the Russian Academy of Sciences in 2009 , the Wolf Prize in 2005 and the Leonhard Euler Gold Medal in 2012 . In 1978 he gave a plenary lecture at the ICM in Helsinki (Linear Operators and Integrable Hamiltonian Systems), was invited speaker at the ICM in Moscow (Pontryagin Classes, the fundamental group and some problems of the stable algebra) in 1966, in Stockholm in 1962 (Smooth manifolds of common homotopy type) and in 1970 at the ICM in Nice (Analogues hermitiens de la K-theorie), but could not attend the congress himself because he had no travel permit due to the support of dissidents. In 1977, 1981, 1986 and 1988 he also gave plenary lectures at the International Congresses for Mathematical Physics. He has been a corresponding member of the Soviet Academy of Sciences since 1966 and a full member since 1981 . He has been an honorary member of the London Mathematical Society since 1987 and of the Serbian Academy of Sciences since 1988. In 1988 he received an honorary doctorate from the University of Athens and in 1999 from the University of Tel Aviv . He has been a member of the Accademia dei Lincei since 1991 , of the Academia Europaea since 1993, of the National Academy of Sciences since 1994, of the Pontifical Academy of Sciences since 1996 and of the European Academy of Sciences since 2003. From 1985 to 1996 he was President of the Moscow Mathematical Society . In 2008/09 and 2009/2010 he was on the Abel Prize Committee .

Fonts

  • Basic elements of differential geometry and topology , Dordrecht, Kluwer 1990
  • with SV Manakov, LP Pitaevskii, VE Zakharov : Theory of solitons: the inverse scattering method . Plenary, New York 1984
  • with Boris Dubrovin , Fomenko : Modern geometry - methods and applications . Volume 1-3. Springer, Graduate Texts in Mathematics (first 1984, 1988, 1990, Volume 1: The geometry of surfaces and transformation groups ; Volume 2: The geometry and topology of manifolds ; Volume 3: Introduction to homology theory ; also the 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 Lecturenotes)
  • with Taimanov: Cobordisms and their application . world scientific, 2007
  • with Wladimir Arnold he is editor and co-author of the series Dynamical systems of the Encyclopedia of mathematical sciences , Springer
  • Topology - general survey . Volume 1 of the topology series of the Encyclopedia of mathematical sciences . Springer 1996
  • Solitons and geometry . Cambridge 1994 (Fermi Lectures)
  • with Viktor M. Bucher : Solitons, geometry and topology - on the crossroads . AMS
  • with Dubrovin, I. Krichever : Topological and Algebraic Geometry Methods in contemporary mathematical physics , Volume 2. Cambridge (edition of Russian review articles)
  • The methods of algebraic topology from the viewpoint of cobordism theory . In: Math. USSR Izv. , Volume 1, 1967, pp. 827-913
  • New ideas in algebraic topology (K-theory and its applications) . In: Uspekhi Mat. Nauk , Volume 20, 1965, pp. 41-66.
  • with Dubrovin, Wladimir Borissowitsch Matwejew : Non-linear equations of Korteweg – de Vries type, finite-zone linear operators, and Abelian varieties . In: Russian Mathematical Surveys , Volume 31, 1976, pp. 59-146
  • Integrability in Mathematics and theoretical pyhsics: solitons . In: Mathematical Intelligencer , Volume 14, 1992, No. 4, pp. 13-21
  • My generation in mathematics . In: Russian Mathematical Surveys , Volume 49, 1994, p. 1
  • The Second Half of the 20th Century and its Conclusion: Crisis in the Physics and Mathematics Community in Russia and in the West . In: AMS Translations , Volume 212, 2004, mi.ras.ru (PDF)

Web links

Individual evidence

  1. ↑ Senior Researcher in his English curriculum Vitum
  2. ↑ Principal Researcher in his English curriculum vitae
personal data
SURNAME Novikov, Sergei Petrovich
ALTERNATIVE NAMES Новиков, Сергей Петрович (Russian)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH March 20, 1938
PLACE OF BIRTH Gorky