Sergei Novikov (mathematician)


Sergei Petrovich Novikov was a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. He became the first Soviet mathematician to receive the Fields Medal in 1970.

Biography

Novikov was born on 20 March 1938 in Gorky, Soviet Union. He grew up in a family of talented mathematicians. His father was Pyotr Sergeyevich Novikov, who gave a negative solution to the word problem for groups. His mother, Lyudmila Vsevolodovna Keldysh, and maternal uncle, Mstislav Vsevolodovich Keldysh, were also important mathematicians.
Novikov entered Moscow State University in 1955 and graduated in 1960. In 1964, he received the Moscow Mathematical Society Award for young mathematicians and defended a dissertation for the Candidate of Science in Physics and Mathematics degree under Mikhail Postnikov at Moscow State University. In 1965, he defended a dissertation for the Doctor of Science in Physics and Mathematics degree there.
Novikov died on 6 June 2024, at the age of 86.

Career

In 1966, Novikov became a corresponding member of the Academy of Sciences of the Soviet Union. In 1971, he became head of the Mathematics Division of the Landau Institute for Theoretical Physics of the USSR Academy of Sciences. In 1983, Novikov was also appointed the head of the Department of Higher Geometry and Topology at Moscow State University. He became President of the Moscow Mathematical Society in 1985 and remained in that role until 1996, when he moved to the University of Maryland College of Computer, Mathematical, and Natural Sciences at the University of Maryland, College Park. He continued to maintain research appointments at the Landau Institute for Theoretical Physics, Moscow State University, and the Department of Geometry and Topology at the Steklov Mathematical Institute after his move to Maryland.

Research

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 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 C. T. C. 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. 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 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 Takahiro Shiota, following earlier work by Enrico Arbarello and Corrado de Concini, and by Motohico Mulase.

Awards and honours

In 1967, Novikov received the Lenin Prize. In 1970, Novikov became the first Soviet mathematician to be awarded the Fields Medal. He was not allowed to travel to the International Congress of Mathematicians in Nice to accept his medal by the Soviet government due to his support for people who had been arrested and sent to mental institutions for speaking out against the regime, but he received it in 1971 when the International Mathematical Union met in Moscow. In 2005, he 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. In 2020, he received the Lomonosov Gold Medal of the Russian Academy of Sciences.
In 1981, he was elected a full member of the USSR Academy of Sciences. He was elected to the London Mathematical Society, Serbian Academy of Sciences and Arts, Accademia dei Lincei, Academia Europaea, National Academy of Sciences, Pontifical Academy of Sciences,, and Montenegrin Academy of Sciences and Arts.
He received honorary doctorates from the University of Athens and University of Tel Aviv.

Writings