Sergei Novikov (mathematician)
| Sergei Petrovich Novikov | |
|---|---|
| Born |
20 March 1938 Gorky, Russian SFSR, Soviet Union |
| Fields | Mathematics |
| Institutions |
Moscow State University Independent University of Moscow Steklov Institute of Mathematics University of Maryland |
| 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 |
| Known for |
Adams–Novikov spectral sequence Krichever–Novikov algebras Morse–Novikov theory Novikov conjecture Novikov ring Novikov–Shubin invariant |
| 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.
Novikov was born on 20 March 1938 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.
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.
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