Dmitry Fuchs
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Dmitry Borisovich Fuchs (Russian: Дмитрий Борисович Фукс, romanized: Dmitry Borisovich Fuks,[1] born 30 September 1939, Kazan,[2] Tatar Autonomous Soviet Socialist Republic) is a Soviet and American mathematician, specializing in the representation theory of infinite-dimensional Lie groups and in topology.[3]
Education and career
[edit | edit source]Fuchs received in 1964 his Russian candidate degree (Ph.D.) under Albert S. Schwarz at Moscow State University,[4] where he taught thereafter. Schwarz conducted a seminar on algebraic topology with Mikhail Postnikov and Vladimir Boltyanski. Fuchs participated in the seminar and, as a student, published papers with Schwarz, as did Askold Ivanovich Vinogradov a few years earlier. Fuchs received his Russian doctorate (higher doctoral degree) in 1987 at Tbilisi State University. Since 1991 he has been a professor at the University of California, Davis.
With Israel Gelfand he introduced in 1970 the Gelfand-Fuchs cohomology of Lie algebras.[5] Gelfand-Fuchs cohomology has applications in the proof of the Macdonald identities in combinatorics and in the calculation of characteristic classes of foliations. With Boris Feigin he determined the structure of Verma modules in the Virasoro algebra representation theory, which has applications in string theory and conformal field theory.[6]
His students include Boris Feigin (with whom he has collaborated extensively), Fedor Malikov, Sergei Tabachnikov, and Vladimir Rokhlin, as well as Edward Frenkel for whom Fuchs was a second advisor.[7] Frenkel, among many others, was affected by the Soviet antisemitism which flourished from 1954 to 1970 (described by Fuchs) and on into the 1980s.[8][9]
In 1978 Fuchs was an Invited Speaker with talk New results on the characteristic classes of foliations at the International Congress of Mathematicians in Helsinki.
Selected publications
[edit | edit source]- with Anatoli T. Fomenko, Viktor L. Gutenmacher: Homotopic topology. Akadémiai Kiadó, Budapest 1986, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Cohomology of infinite-dimensional Lie algebras. Consultants Bureau, New York NY 1986, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)..
- 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, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)., pp. 65–74.
- with Serge Tabachnikov: Mathematical omnibus. Thirty lectures on classic mathematics. American Mathematical Society, Providence RI 2007, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
Sources
[edit | edit source]- Alexander Astashkevich, Serge Tabachnikov (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, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)..
References
[edit | edit source]- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ Comprehensive Biographical Encyclopedia (in Russian)
- ^ Dmitry B. Fuchs, Mathematics, University of California, Davis
- ^ Dmitry Borisovich Fuchs at the Mathematics Genealogy Project
- ^ Israel M. Gel'fand, Dmitry B. Fuks: Cohomologies of Lie algebra of tangential vector fields of a smooth manifold. In: Functional Analysis and its Applications. vol. 3, no. 3, 1969, pp. 194–210, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).. Israel M. Gel'fand, Dmitry B. Fuks: Cohomology of the Lie algebra of formal vector fields. In: Mathematics of the USSR. Izvestija. vol. 4, no. 2, 1970, pp. 327–340, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)..
- ^ with Fedor G. Malikov and Boris L. Feigin: Singular vectors in Verma modules over Kac—Moody algebras. In: Functional Analysis and its Applications. vol. 20, no. 2, 1986, pp. 103–113, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).. Boris L. Feigin, Dmitry B. Fuchs: Representations of the Virasoro Algebra. In: Anatolii M. Vershik, Dmitrii P. Zhelobenko (eds.): Representation of Lie groups and related topics (= Advanced Studies in Contemporary Mathematics. vol. 7). Gordon and Breach, New York NY 1990, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)., pp. 465–554.
- ^ Fuchs also lectured at the unofficial Jewish University in Moscow at the Institute for Petrochemical and Natural Gas Industry. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (mention of Soviet antisemitism at 3:16:30 of 3:46:38 in video)
External links
[edit | edit source]Lua error in Module:Authority_control at line 153: attempt to index field 'wikibase' (a nil value).