Person: Novikov (2), Sergei
Sergei Novikov is a Russian mathematician who worked in algebraic topology and soliton theory. He won a Fields medal in 1970 and a Wolf prize in 2005.
Mathematical Profile (Excerpt):
- Both of Sergei's parents came from families with remarkable mathematical talents and several other members were noteworthy.
- Despite his high involvement with mathematics, or more likely because of it, Sergei was uncertain for many years whether he wanted to follow a career in the subject.
- When he reached the age of seventeen Sergei finally decided that he wanted to follow a career in mathematics.
- V A Uspenskii, a pupil of Kolmogorov, organised a seminar during Novikov's first year as a student in which problems in set theory, mathematical logic, and functions of a real variable were studied.
- Before beginning his second year of study Novikov had to choose a specialist topic and a supervisor.
- Topology, on the other hand, was not such an important topic at that time as far as Moscow University was concerned, so when Postnikov went to China for the academic year 1958-59, Novikov was left without a supervisor.
- Novikov's first important publication in 1959 Cohomology of the Steenrod algebra, published in Doklady Akademii Nauk SSSR, developed further Adams's methods and results.
- Another important paper Some problems in the topology of manifolds connected with the theory of Thom spaces was published by Novikov in 1960.
- Novikov obtained his first degree in 1960 and then became a research student at the Steklov Institute of Mathematics in Moscow.
- In this respect Novikov was fortunate since Milnor, Hirzebruch and Smale all visited the USSR during the summer of 1961 to attend various conferences.
- Inspired by his meetings in the summer of 1961, Novikov solved a major problem in the autumn of that year.
- By that time Browder had, independently, discovered similar techniques to those Novikov had developed.
- Novikov received an award from the USSR Academy of Sciences in 1964 for this work and he was awarded his doctorate in the same year.
- In 1963 Novikov had been appointed to the staff of the Steklov Institute of Mathematics and, the following year, he was also appointed to the Department of Differential Geometry at Moscow University.
- Novikov became head of the Mathematics Division at the L D Landau Institute for Theoretical Physics of the USSR Academy of Sciences in 1971.
- Novikov also became head of the Department of Higher Geometry and Topology of Moscow University in 1983 and, the following year he became head of the Department of Geometry and Topology of the Mathematical Institute of the USSR Academy of Sciences.
- Novikov's work up to 1971 was on algebraic and differential topology; in particular he studied calculating stable homotopy groups and classifying smooth simply-connected manifolds of dimension greater than 4.
- In 1965 Novikov proved his famous theorem on the invariance of Pontryagin classes and stated the conjecture, now known as the Novikov conjecture, concerning the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group.
- Novikov's original motivation was the theory, in the simply connected case, of Browder-Novikov and Wall, which led to the classification of manifolds in high dimensions.
- Novikov discussed his conjecture in a lecture given at the 1970 International Congress of Mathematicians in Nice where he received a Fields Medal.
- After 1971 Novikov became interested in mathematical physics and dynamical systems.
- Novikov has received many honours for his outstanding work.
- Many societies have honoured Novikov with membership such as the London Mathematical Society in 1987 and the Pontifical Academy of Sciences in 1996.
- In the early 1970s Novikov turned his attention to mathematical physics, initially contributing to general relativity and conductivity of metals.
- These include a systematic study of finite-gap solutions of two-dimensional integrable systems, formulation of the equivalence of the classification of algebraic-geometric solutions of the KP equation with the conformal classification of Riemann surfaces, and work (with Krichever) on "almost commuting" operators that appear in string theory and matrix models ("Krichever-Novikov algebras", now widely used in physics).
- Novikov made a fundamental and striking contribution to two separate fields in mathematics, while he is one of those rare mathematicians who brings deep, key mathematical ideas to bear on difficult pivotal problems of physics, in ways that are stunning and compelling for both mathematicians and physicists.
Born 20 March 1938, Gorky (now Nizhny Novgorod), Russia.
View full biography at MacTutor
Tags relevant for this person:
Prize Fields Medal, Origin Russia, Topology, Prize Wolf
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
