Sergei Petrovich Novikov (also Serguei) ( Russian: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

and

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-ei ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, noted for work in both

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...

and soliton theory. In 1970, he won the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

Early life

Novikov was born on 20 March 1938 in Gorky,

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nationa ...

(now

Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət ), colloquially shortened to Nizhny, from the 13th to the 17th century Novgorod of the Lower Land, formerly known as Gork ...

). 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 In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group ''G'' is the algorithmic problem of deciding whether two words in the generators represent the same el ...

. His mother, Lyudmila Vsevolodovna Keldysh, and maternal uncle,

Mstislav Vsevolodovich Keldysh Mstislav Vsevolodovich Keldysh (russian: Мстисла́в Все́володович Ке́лдыш; – 24 June 1978) was a Soviet mathematician who worked as an engineer in the Soviet space program. He was the academician of the Academy ...

, were also important mathematicians. In 1955 Novikov entered

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

, 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 PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * '' Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. al ...

) 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.

Research in topology

Novikov's early work was in

cobordism theory In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same d ...

, in relative isolation. Among other advances he showed how the

Adams spectral sequence In mathematics, the Adams spectral sequence is a spectral sequence introduced by which computes the stable homotopy groups of topological spaces. Like all spectral sequences, it is a computational tool; it relates homology theory to what is now c ...

, a powerful tool for proceeding from

homology theory In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topolog ...

to the calculation of

homotopy group In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homotop ...

s, 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 operation In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if ''F'' is a functor defining a cohomology theory, then a coho ...

s in the general setting, since the basis of the spectral sequence is the initial data of

Ext functor In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological algebra, in which ideas from algebraic topology are used to define invariants of algebraic stru ...

s taken with respect to a ring of such operations, generalising the

Steenrod algebra In algebraic topology, a Steenrod algebra was defined by to be the algebra of stable cohomology operations for mod p cohomology. For a given prime number p, the Steenrod algebra A_p is the graded Hopf algebra over the field \mathbb_p of order p, ...

. The resulting Adams–Novikov spectral sequence is now a basic tool in

stable homotopy theory In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the F ...

. Novikov also carried out important research in

geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originate ...

, being one of the pioneers with William Browder,

Dennis Sullivan Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate C ...

, and C. T. C. Wall of the

surgery theory In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by . Milnor called this technique ''surgery'', while And ...

method for classifying high-dimensional manifolds. He proved the topological invariance of the rational

Pontryagin class In mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology groups with degrees a multiple of four. Definition Given a real vector bundle ...

es, and posed the Novikov conjecture. This work was recognised by the award in 1970 of the

. He was not allowed to travel to

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative ...

to accept his medal, but he received it in 1971 when the

International Mathematical Union The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...

met in Moscow. From about 1971 he moved to work in the field of isospectral flows, with connections to the theory of

theta function In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field ...

s. 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 In mathematics and physics, the Kadomtsev–Petviashvili equation (often abbreviated as KP equation) is a partial differential equation to describe nonlinear wave motion. Named after Boris Borisovich Kadomtsev and Vladimir Iosifovich Petviashv ...

of soliton theory. This was proved by Takahiro Shiota (1986), following earlier work by

Enrico Arbarello Enrico Arbarello is an Italian mathematician who is a leading expert in algebraic geometry. He earned a Ph.D. at Columbia University in New York in 1973. He was a visiting scholar at the Institute for Advanced Study from 1993-94. He is now a M ...

and Corrado de Concini (1984), and by Motohico Mulase (1984).

Later career

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 The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...

since 1991). In 1982 Novikov was also appointed the ''Head of the Chair in Higher Geometry and Topology'' at the

. In 1984 he was elected as a member of

Serbian Academy of Sciences and Arts The Serbian Academy of Sciences and Arts ( la, Academia Scientiarum et Artium Serbica, sr-Cyr, Српска академија наука и уметности, САНУ, Srpska akademija nauka i umetnosti, SANU) is a national academy and the ...

. , 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 The College of Computer, Mathematical, and Natural Sciences (CMNS) at the University of Maryland, College Park, is home to ten academic departments and a dozen interdisciplinary research centers and institutes. CMNS is one of 13 schools and colleg ...

University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of ...

and is a Principal Researcher of the Landau Institute for Theoretical Physics in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

. In 2005 Novikov was awarded the

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of nati ...

for his contributions to

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

and to

mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...

. 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 The Lomonosov Gold Medal (russian: Большая золотая медаль имени М. В. Ломоносова ''Bol'shaya zolotaya medal' imeni M. V. Lomonosova''), named after Russian scientist and polymath Mikhail Lomonosov, is awarded ...

of the Russian Academy of Sciences.Lomonosov Gold Medal 2020
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Writings

* * * 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.
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 Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pr ...

1981 (London Math. Society Lecture notes) * * with V. I. 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

References

External links

Homepage
and Curriculum Vitae on the website of Steklov Mathematical Institute
Biography (in Russian)
on the website of