Sergei Petrovich Novikov
Encyclopedia
Sergei Petrovich Novikov (also Serguei) (Russian
: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a Soviet and Russia
n mathematician
, noted for work in both algebraic topology
and soliton theory.
, Soviet Union
(now Nizhny Novgorod
, Russia
).
He grew up in a family of talented mathematicians. His father was Pyotr Novikov, who gave the negative solution of the word problem for groups
. His mother Ludmila Vsevolodovna Keldysh and maternal uncle Mstislav Vsevolodovich Keldysh
were also important mathematicians.
In 1955 Novikov entered Moscow State University
(graduating 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 at the Moscow State University (it is equivalent to the PhD
). 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 USSR Academy of Sciences.
, a powerful tool for proceeding from homology theory
to the calculation of homotopy group
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
s in the general setting, since the basis of the spectral sequence is the initial data of Ext functor
s 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 Terry Wall of the surgery theory
method for classifying high-dimensional manifolds. He proved the topological invariance of the rational Pontryagin class
es, and posed the Novikov conjecture
. This work was recognised by the award in 1970 of the Fields Medal
. 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 Shiota
(1986), following earlier work by Arbarello
and de Concini (1984), and by Mulase (1984).
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
.
, Novikov is the Head of the Department of geometry and topology at the Steklov Mathematical Institute
. He is also a Distinguished University Professor at University of Maryland, College Park
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
. He is one of just eleven mathematicians who received both the Fields Medal and the Wolf Prize.
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a Soviet and Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, noted for work in both algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which 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 up to homotopy equivalence.Although algebraic topology...
and soliton theory.
Early life
Novikov was born in GorkyNizhny Novgorod
Nizhny Novgorod , colloquially shortened to Nizhny, is, with the population of 1,250,615, the fifth largest city in Russia, ranking after Moscow, St. Petersburg, Novosibirsk, and Yekaterinburg...
, Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
(now Nizhny Novgorod
Nizhny Novgorod
Nizhny Novgorod , colloquially shortened to Nizhny, is, with the population of 1,250,615, the fifth largest city in Russia, ranking after Moscow, St. Petersburg, Novosibirsk, and Yekaterinburg...
, Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
).
He grew up in a family of talented mathematicians. His father was Pyotr Novikov, who gave the negative solution of the word problem for groups
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 element...
. His mother Ludmila Vsevolodovna Keldysh and maternal uncle Mstislav Vsevolodovich Keldysh
Mstislav Keldysh
Mstislav Vsevolodovich Keldysh was a Soviet scientist in the field of mathematics and mechanics, academician of the USSR Academy of Sciences , President of the USSR Academy of Sciences , three times Hero of Socialist Labor , fellow of the Royal Society of Edinburgh . He was one of the key figures...
were also important mathematicians.
In 1955 Novikov entered Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
(graduating in 1960). Four years later he received the Moscow Mathematical Society
Moscow Mathematical Society
The Moscow Mathematical Society is a society of Moscow mathematicians aimed at the development of mathematics in Russia.The first meeting of the society was . Nikolai Brashman was the first president of MMO. Victor Vassiliev is the current president of MMO....
Award for young mathematicians. In the same year he defended a dissertation for the Candidate of Science in Physics and Mathematics degree at the Moscow State University (it is equivalent to the PhD
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...
). 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 USSR Academy of Sciences.
Research in topology
Novikov's early work was in cobordism theory, in relative isolation. Among other advances he showed how the Adams spectral sequenceAdams spectral sequence
In mathematics, the Adams spectral sequence is a spectral sequence introduced by . Like all spectral sequences, it is a computational tool; it relates homology theory to what is now called stable homotopy theory...
, a powerful tool for proceeding from homology theory
Homology theory
In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of homology theories on topological spaces.-The general idea:...
to the calculation of homotopy group
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, which records information about loops in a space...
s, could be adapted to the new (at that time) cohomology theory typified by cobordism and K-theory
K-theory
In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
. This required the development of the idea of cohomology operation
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 cohomology operation should be a natural transformation from...
s in the general setting, since the basis of the spectral sequence is the initial data of Ext functor
Ext functor
In mathematics, the Ext functors of homological algebra are derived functors of Hom functors. They were first used in algebraic topology, but are common in many areas of mathematics.- Definition and computation :...
s taken with respect to a ring of such operations, generalising the Steenrod algebra
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 Ap is the graded Hopf algebra over the field Fp of order p, consisting of all stable cohomology operations for mod p...
. The resulting Adams–Novikov spectral sequence is now a basic tool in stable homotopy theory
Stable homotopy theory
In mathematics, stable homotopy theory is that part of homotopy theory concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor...
.
Novikov also carried out important research in geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
, being one of the pioneers with William Browder
William Browder (mathematician)
William Browder is an American mathematician, specializing in algebraic topology, differential topology and differential geometry...
, Dennis Sullivan
Dennis Sullivan
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.-Work in topology:He...
and Terry Wall of the surgery theory
Surgery theory
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a 'controlled' way, introduced by . Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along...
method for classifying high-dimensional manifolds. He proved the topological invariance of the rational Pontryagin class
Pontryagin class
In mathematics, the Pontryagin classes are certain characteristic classes. The Pontryagin class lies in cohomology groups with degree a multiple of four...
es, and posed the Novikov conjecture
Novikov conjecture
The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965....
. This work was recognised by the award in 1970 of the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
. 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 Shiota
Takahiro Shiota
is a Japanese mathematician at Kyoto University. In 1986, he proved Novikov's conjecture about the Riemann–Schottky problem by characterization of Jacobian varieties.Shiota obtained his doctorate at Harvard University in 1984....
(1986), following earlier work by Arbarello
Enrico Arbarello
Enrico Arbarello is an Italian mathematician, considered one of the best experts of the algebraic varieties.He got a degree in Rome in 1969, then a Ph.D. at the Columbia University of New York in 1973....
and de Concini (1984), and by Mulase (1984).
Later career
Since 1971 Novikov has worked at the Landau Institute for Theoretical PhysicsLandau Institute for Theoretical Physics
The L. D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences is a research institution, located in the small town of Chernogolovka near Moscow...
of the USSR Academy of Sciences. In 1981 he was elected a Full Member of the USSR Academy of Sciences (Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
since 1991).
In 1982 Novikov was also appointed the Head of the Chair in Higher Geometry and Topology at the Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
.
In 1984 he was elected as a member of Serbian Academy of Sciences and Arts
Serbian Academy of Sciences and Arts
The Serbian Academy of Sciences and Arts is the most prominent academic institution in Serbia today...
.
, Novikov is the Head of the Department of geometry and topology at the Steklov Mathematical Institute
Steklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. It was established April 24, 1934 by the decision of the General Assembly of the Academy of Sciences of the USSR in...
. He is also a Distinguished University Professor at University of Maryland, College Park
University of Maryland, College Park
The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...
and is a Principal Researcher of the Landau Institute for Theoretical Physics
Landau Institute for Theoretical Physics
The L. D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences is a research institution, located in the small town of Chernogolovka near Moscow...
in Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
.
In 2005 Novikov was awarded the Wolf Prize for his contributions to algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which 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 up to homotopy equivalence.Although algebraic topology...
, differential topology
Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.- Description :...
and to mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
. He is one of just eleven mathematicians who received both the Fields Medal and the Wolf Prize.
External links
- Homepage and Curriculum Vitae on the website of Steklov Mathematical Institute
- Biography (in Russian) on the website of Moscow State UniversityMoscow State UniversityLomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...