The Laureates

Copyright © Klaus Tschira Stiftung / Peter Badge

Sergei Novikov

Born 20 March 1938 in Gorky (today Nizhny, Novgorod, Russia)

Fields Medal (1970) for the proof of the topological invariance of the rational Pontryagin classes of differentiable manifolds (1965), as well as his calculations of the homotopy groups of Thom spaces and cobordism rings, development of the new powerful  method of studying stable homotopy groups of spheres, classification of multidimensional simply connected manifolds and proof of the existence of compact leaf for 2- foliations of the 3-sphere.  Novikov’s Higher Signature Conjecture over 40 years attracts attention of many scientists as a central problem of multidimensional differential topology.

(Soviet Math authorities did not allow Novikov to attend Fields Medal Ceremony at the Math Congress in Nice, 1970, because he signed a letter supporting A.S.Esenin-Volpin mathematician, dissident and son of the famous russian poet S. Esenin. Esenin-Volpin was arrested and sent to mental hospital. Novikov’s career in USSR was stopped for 10 years.)

There are families in which mathematical talent abounds. The Bernoullis are one example, and equally so the family of Sergei Novikov: not only was his father a mathematician who solved for example the word problem for groups, his mother, Lyudmila Keldysh, was a professor of mathematics who provided significant contributions to geometric topology. The wider family too were mathematicians — Novikov’s uncle Mstislav Keldysh (one of leading scientists responsible for the sputnik program in 1950s) was since 1961 for many years president of the Academy of Sciences of the USSR, while his two brothers studied mathematics and physics. One of them, Leonid Keldysh, is a prominent quantum solid state physicist, full member of Russian Academy  of Sciences and Foreign Associate of the National Academy of Sciences of USA.

Novikov started his studies in 1955 at the prestigious Moscow State (Lomonosov) University and graduated from there in 1960 with masters thesis in the cobordism theory. In 1964 he was awarded the prize for young mathematicians of the Moscow Mathematical Society for the classification of multidimensional manifolds and published his doctorate about differentiable sphere bundles in the same year under supervision of Mikhail Postnikov. Novikov earned his habilitation and proved topological invariance of rational Pontryagin classes in 1965.

The following year he  became Corresponding Member of the Academy of Sciences of the USSR (and in 1981 a full member). From 1964 to 1975 Novikov worked at the Steklov Institute as a Research scientist, from 1965 as a Senior research scientist. He was also employed at Mekh-Mat, the Department of Mathematics and Mechanics at Moscow State University, and took a full professorship there in 1967. From 1971 to 1993 Novikov headed the mathematics group of the Landau Institute for Theoretical Physics of the Academy of Sciences, and after that continued to work there as a Principal research scientist.

From 1983 onwards he headed the group for geometry and topology at Moscow University and from 1984 onwards at the Steklov Institute as well. He was a visiting professor at the Ecole Normale Superieure (1991), the University of Maryland, College Park (1992-1996), the “KIAS” in Seoul (2000 to 2002) and the Isaac Newton Institute in Cambridge (2009). Novikov has been Distinguished University Professor at the University of Maryland (USA) since 1997.

Sergei Novikov is the recipient of numerous prizes and honorary memberships, including the Lenin Prize (1967), the Lobachevskii Prize of the Academy of Sciences of the USSR (1981), the Wolf Prize for Mathematics (along with Grigori Margulis, 2005), the Pogorelov Prize of the Ukrainian National Academy of Sciences (2008), the Bogoliubov Gold Medal of the Russian Academy of Sciences and the Institute for Nuclear Research at  Dubna (2009), and the Euler medal of the Russian Academy of Sciences (2012). He is an honorary member of the London Mathematical Society(1987) and Honorary President of the Moscow  Mathematical Society (2010), Foreign Associate of the National Academy of Sciences of the USA (1994), Member of the Pontifical Academy of Sciences of the Vatican (1996), Foreign Member of the Academia dei  Lincei  in Italy (1991), Serbian Academy of Art and Scieces (1988), Montenegrian  Academy of Art and Sciences (2011), Member of Academia Europea (1993), Fellow of the European Academy of Sciences in Brussels (2003) and holds honorary doctorates from the universities of Athens (1988) and Tel Aviv (1999).

Sergei P. Novikov today conducts research especially in the areas of topology and mathematical physics, after gaining a number of important results in algebraic and differential topology.

From the 1970s he dealt with, among other things, Morse theory, a branch of Topology and Calculus of Variations. Novikov constructed a Multivalued analog of this theory for manifolds and mapping spaces (1981), which in turn now play an important role in modern quantum field theory. It was also used by Novikov and his school in the study  topological phenomena in the magnetoresistance for  single crystal metals (1997-2000).

Novikov also brought numerous methods from algebraic geometry into physics. Of particular importance was, for example, his discovery of  algebro-geometric (periodic)  solutions to the famous KdV (Korteweg-De Vries) and similar soliton equations  in the theory of nonlinear waves (1974). Joint activity of Novikov with Boris Dubrovin and Igor Krichever  led to the bridge between the KP (Kadomtsev-Petviashvili) equation  in mathematical physics and classical Riemann-Schottki Problem in the theory of Theta-functions (1980).

Together with Igor Krichever, he invented an analog of Fourier and Laurent bases on  Riemann Surfaces, forming new type of algebras, known as Krichever-Novikov algebras, with wide application in physics today (1990).

Sergei Novikov married Eleonora Tsoi in 1962. She also is a mathematician who finished MekhMat in Moscow State University and worked many years teaching mathematics. They have 3 children, two girls (Irina and Maria) and one son (Peter).None of them are scientists.

Novikov is a great lover of history. It is his main hobby.