Dmitry Borisovich Fuchs (Дмитрий Борисович Фукс, born 30 September 1939,

Kazan Kazan ( ; rus, Казань, p=kɐˈzanʲ; tt-Cyrl, Казан, ''Qazan'', IPA: ɑzan is the capital and largest city of the Republic of Tatarstan in Russia. The city lies at the confluence of the Volga and the Kazanka rivers, covering ...

Tatar Autonomous Soviet Socialist Republic The Tatar Autonomous Soviet Socialist Republic (russian: Татарская Автономная Советская Социалистическая Республика; tt-Cyrl, Татарстан Автономияле Совет Соци� ...

) is a Russian-American mathematician, specializing in the representation theory of infinite-dimensional

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the addit ...

s and in topology.

Education and career

Fuchs received in 1964 his Russian candidate degree (Ph.D.) under

Albert S. Schwarz Albert Solomonovich Schwarz (; russian: А. С. Шварц; born June 24, 1934) is a Soviet and American mathematician and a theoretical physicist educated in the Soviet Union and now a professor at the University of California, Davis. Early li ...

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 ...

, where he taught thereafter. Schwarz conducted a seminar on algebraic topology with

Mikhail Postnikov Mikhail Mikhailovich Postnikov (russian: Михаи́л Миха́йлович По́стников; 27 October 1927 – 27 May 2004) was a Soviet mathematician, known for his work in algebraic and differential topology. Biography He was bor ...

and

Vladimir Boltyanski Vladimir Grigorevich Boltyansky (russian: Влади́мир Григо́рьевич Болтя́нский; 26 April 1925 – 16 April 2019), also transliterated as Boltyanski, Boltyanskii, or Boltjansky, was a Soviet and Russian mathematicia ...

. Fuchs participated in the seminar and, as a student, published papers with Schwarz, as did

Askold Ivanovich Vinogradov Askold Ivanovich Vinogradov (russian: Аско́льд Ива́нович Виногра́дов) (1929 – 31 December 2005) was a Russian mathematician working in analytic number theory. The Bombieri–Vinogradov theorem In mathematics, the ...

a few years earlier. Fuchs received his Russian doctorate (higher doctoral degree) in 1987 at

Tbilisi State University Ivane Javakhishvili Tbilisi State University ( ka, ივანე ჯავახიშვილის სახელობის თბილისის სახელმწიფო უნივერსიტეტი ''Ivane Javaxishvi ...

. Since 1991 he has been a professor at the

University of California, Davis The University of California, Davis (UC Davis, UCD, or Davis) is a public land-grant research university near Davis, California. Named a Public Ivy, it is the northernmost of the ten campuses of the University of California system. The inst ...

. With

Israel Gelfand Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гел� ...

he introduced in 1970 the Gelfand-Fuchs cohomology of Lie algebras. Gelfand-Fuchs cohomology has applications in the proof of the

Macdonald identities In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by . They include as special cases the Jacobi triple product identity, Watson's quintuple product identity In mathematic ...

in combinatorics and in the calculation of characteristic classes of

foliation In mathematics ( differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition ...

s. With

Boris Feigin Boris Lvovich Feigin (russian: Бори́с Льво́вич Фе́йгин) (born 20 November 1953) is a Russian mathematician. His research has spanned representation theory, mathematical physics, algebraic geometry, Lie groups and Lie algebras ...

he determined the structure of

Verma module Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. Sp ...

s in the

Virasoro algebra In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string t ...

representation theory, which has applications in string theory and

conformal field theory A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometime ...

. His students include Boris Feigin (with whom he has collaborated extensively), Fedor Malikov,

Sergei Tabachnikov Sergei Tabachnikov, also spelled Serge, (in Russian: Сергей Львович Табачников; born in 1956) is a Russian mathematician who works in geometry and dynamical systems. He is currently a Professor of Mathematics at Pennsylvan ...

, and Vladimir Rokhlin, as well as Edward Frenkel for whom Fuchs was a second advisor.Fuchs also lectured at the unofficial ''Jewish University'' in Moscow at the Institute for Petrochemical and Natural Gas Industry. In 1978 he was an Invited Speaker with talk ''New results on the characteristic classes of foliations'' at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Helsinki Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...

Selected publications

* with Anatoli T. Fomenko, Viktor L. Gutenmacher: ''Homotopic topology.'' Akadémiai Kiadó, Budapest 1986, . * ''Cohomology of infinite-dimensional Lie algebras.'' Consultants Bureau, New York NY 1986, . * ''Singular vectors over the Virasoro Algebra and extended Verma Modules.'' In: Dmitry Fuchs (ed.): ''Unconventional Lie Algebras'' (= ''Advances in Soviet Mathematics.'' vol. 17). American Mathematical Society, Providence RI 1993, , pp. 65–74. * with Serge Tabachnikov
''Mathematical omnibus. Thirty lectures on classic mathematics.''
American Mathematical Society, Providence RI 2007,

Sources

* Alexander Astashkevich,

Serge Tabachnikov Sergei Tabachnikov, also spelled Serge, (in Russian: Сергей Львович Табачников; born in 1956) is a Russian mathematician who works in geometry and dynamical systems. He is currently a Professor of Mathematics at Pennsylvani ...

(eds.)
''Differential topology, infinite-dimensional lie algebras, and applications. D. B. Fuchs' 60th Anniversary Collection''
(= ''American Mathematical Society. Translations.'' Series 2, 194). American Mathematical Society, Providence RI 1999, .

References

External links

{{DEFAULTSORT:Fuchs, Dmitry 1939 births Living people 20th-century Russian mathematicians 20th-century American mathematicians 21st-century American mathematicians Moscow State University alumni Moscow State University faculty Tbilisi State University faculty University of California, Davis faculty Mathematicians from Kazan