Sergei Petrovich Novikov | |
---|---|

Born | |

Alma mater | Moscow State University |

Known for | Adams–Novikov spectral sequence Krichever–Novikov algebras Morse–Novikov theory Novikov conjecture Novikov ring Novikov–Shubin invariant Novikov–Veselov equation Novikov's compact leaf theorem |

Awards | Lenin Prize (1967) Fields Medal (1970) Lobachevsky Medal (1981) Wolf Prize (2005) Lomonosov Gold Medal (2020) |

Scientific career | |

Fields | Mathematics |

Institutions | Moscow State University Independent University of Moscow Steklov Institute of Mathematics University of Maryland |

Doctoral advisor | Mikhail Postnikov |

Doctoral students | Victor Buchstaber Boris Dubrovin Sabir Gusein-Zade Gennadi Kasparov Alexander Mishchenko Iskander Taimanov Anton Zorich Fedor Bogomolov |

**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).^{ [1] }

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.^{ [1] }

In 1955 Novikov entered Moscow State University, from which he graduated 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 (equivalent to the PhD) at Moscow State University. 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 Academy of Sciences of the Soviet Union.

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.^{ [2] }^{ [3] }

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. This work was recognised by the award in 1970 of the Fields Medal. He was not allowed to travel to Nice to accept his medal, but he received it in 1971 when the International Mathematical Union met in Moscow. 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 (characterizing principally polarized abelian varieties that are the Jacobian of some algebraic curve) 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 (1986),^{ [4] } following earlier work by Enrico Arbarello and Corrado de Concini (1984),^{ [5] } and by Motohico Mulase (1984).^{ [6] }

Since 1971 Novikov has worked at the Landau Institute for Theoretical Physics of the USSR Academy of Sciences. In 1981 he was elected a Full Member of the USSR Academy of Sciences (Russian Academy of Sciences since 1991). In 1982 Novikov was also appointed the *Head of the Chair in Higher Geometry and Topology* at the Moscow State University.

In 1984 he was elected as a member of Serbian Academy of Sciences and Arts.

As of 2004^{ [update] }, Novikov is the Head of the Department of geometry and topology at the Steklov Mathematical Institute. He is also a Distinguished University Professor for the Institute for Physical Science and Technology, which is part of the University of Maryland College of Computer, Mathematical, and Natural Sciences at University of Maryland, College Park ^{ [7] } and is a Principal Researcher of the Landau Institute for Theoretical Physics in Moscow.

In 2005 Novikov was awarded the Wolf Prize for his contributions to algebraic topology, differential topology and to mathematical physics.^{ [8] } 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.^{ [9] }

*Basic elements of differential geometry and topology*, Dordrecht, Kluwer 1990; 2013 pbk edition (with A. T. Fomenko)- with S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov:
*Theory of solitons: the inverse scattering method*, New York 1984 - with Dubrovin and Fomenko:
*Modern geometry- methods and applications*, Vol.1-3, Springer, Graduate Texts in Mathematics (originally 1984, 1988, 1990, V.1 The geometry of surfaces and transformation groups, V.2 The geometry and topology of manifolds, V.3 Introduction to homology theory) -
*Topics in Topology and mathematical physics*, AMS (American Mathematical Society) 1995 *Integrable systems - selected papers*, Cambridge University Press 1981 (London Math. Society Lecture notes)- with Taimanov:
*Cobordisms and their applications*, 2007, World Scientific - with Arnold as editor and co-author:
*Dynamical systems*, 1994, Encyclopedia of mathematical sciences, Springer *Topology I: general survey*, V. 12 of Topology Series of Encyclopedia of mathematical sciences, Springer 1996; 2013 edition-
*Solitons and geometry*, Cambridge 1994 - as editor, with Buchstaber:
*Solitons, geometry and topology: on the crossroads*, AMS, 1997 - with Dubrovin and Krichever:
*Topological and Algebraic Geometry Methods in contemporary mathematical physics*V.2, Cambridge *My generation in mathematics*, Russian Mathematical Surveys V.49, 1994, p. 1 doi : 10.1070/RM1994v049n06ABEH002446

**Vladimir Igorevich Arnold** was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics—KAM theory, and topological Galois theory.

**Anatoly Timofeevich Fomenko** is a Soviet and Russian mathematician, professor at Moscow State University, well known as a topologist, and a member of the Russian Academy of Sciences. He is the author of a pseudoscientific theory known as New Chronology, based on works of Russian-Soviet writer and freemason Nikolai Alexandrovich Morozov. He is also a member of the Russian Academy of Natural Sciences (1991).

**Sir Simon Kirwan Donaldson** is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.

In mathematics, **complex cobordism** is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it directly one uses some slightly weaker theories derived from it, such as Brown–Peterson cohomology or Morava K-theory, that are easier to compute.

**Vladimir Gershonovich Drinfeld**, surname also romanized as **Drinfel'd**, is a renowned mathematician from the former USSR, who emigrated to the United States and is currently working at the University of Chicago.

**Yuri Ivanovich Manin** is a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics. Moreover, Manin was one of the first to propose the idea of a quantum computer in 1980 with his book *Computable and Uncomputable*.

**Victor Matveevich Buchstaber** is a Soviet and Russian mathematician known for his work on algebraic topology, homotopy theory, and mathematical physics.

**William Browder** is an American mathematician, specializing in algebraic topology, differential topology and differential geometry. Browder was one of the pioneers with Sergei Novikov, Dennis Sullivan and C. T. C. Wall of the surgery theory method for classifying high-dimensional manifolds. He served as President of the American Mathematical Society until 1990.

In mathematics, **secondary calculus** is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and employing algebraic methods.

**Vladimir Abramovich Rokhlin** was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry, measure theory, probability theory, ergodic theory and entropy theory.

**Jack Johnson Morava** is an American homotopy theorist at Johns Hopkins University.

**Matthias Kreck** is a German mathematician who works in the areas of Algebraic Topology and Differential topology. From 1994 to 2002 he was director of the Mathematical Research Institute of Oberwolfach and from October 2006 to September 2011 he was the director of the Hausdorff Center for Mathematics at the University of Bonn, where he is currently a professor.

**Peter Steven Landweber** is an American mathematician working in algebraic topology.

**Vladimir Ilyin** (1928—2014) was a Russian mathematician, Professor at Moscow State University, Doctor of Science, Academician of the Russian Academy of Sciences who made significant contributions to the theory of differential equations, the spectral theory of differential operators, and mathematical modeling.

**Boris Anatolievich Dubrovin** was a Russian mathematician, Doctor of Physical and Mathematical Sciences (1984).

**Henri Moscovici** is a Romanian-American mathematician, specializing in non-commutative geometry and global analysis.

**Alexandre Mikhailovich Vinogradov** was a Russian and Italian mathematician. He made important contributions to the areas of differential calculus over commutative algebras, the algebraic theory of differential operators, homological algebra, differential geometry and algebraic topology, mechanics and mathematical physics, the geometrical theory of nonlinear partial differential equations and secondary calculus.

**Dan Burghelea** is a Romanian-American mathematician, academic, and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.

**Alexandr Sergeevich Mishchenko** is a Russian mathematician, specializing in differential geometry and topology and their applications to mathematical modeling in the biosciences.

- 1 2 O'Connor, John J.; Robertson, Edmund F., "Sergei Petrovich Novikov",
*MacTutor History of Mathematics archive*, University of St Andrews - ↑ Zahler, Raphael (1972). "The Adams-Novikov Spectral Sequence for the Spheres".
*Annals of Mathematics*.**96**(3): 480–504. doi:10.2307/1970821. JSTOR 1970821. - ↑ Botvinnik, Boris I. (1992).
*Manifolds with Singularities and the Adams-Novikov Spectral Sequence*. Cambridge University Press. p. xi. ISBN 9780521426084. - ↑ Shiota, Takahiro (1986). "Characterization of Jacobian varieties in terms of soliton equations".
*Inventiones Mathematicae*.**83**(2): 333–382. Bibcode:1986InMat..83..333S. doi:10.1007/BF01388967. S2CID 120739493. - ↑ Arbarello, Enrico; De Concini, Corrado (1984). "On a set of equations characterizing Riemann matrices".
*Annals of Mathematics*.**120**(1): 119–140. doi:10.2307/2007073. JSTOR 2007073. - ↑ Mulase, Motohico (1984). "Cohomological structure in soliton equations and Jacobian varieties".
*Journal of Differential Geometry*.**19**(2): 403–430. doi: 10.4310/jdg/1214438685 . MR 0755232. - ↑ "Faculty/Staff Directory Search".
*University of Maryland*. Retrieved 22 April 2016. - ↑ The Wolf Foundation – "Sergei P. Novikov Winner of Wolf Prize in Mathematics - 2005"
- ↑ Lomonosov Gold Medal 2020

- Homepage and Curriculum Vitae on the website of Steklov Mathematical Institute
- Biography (in Russian) on the website of Moscow State University
- O'Connor, John J.; Robertson, Edmund F., "Sergei Novikov (mathematician)",
*MacTutor History of Mathematics archive*, University of St Andrews - Sergei Novikov at the Mathematics Genealogy Project

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.