Dmitry Fuchs

Dmitry Fuchs (right) with Sergei Tabatschnikow, Oberwolfach 2006

Dmitry Borisovich Fuchs (also: DB Fuks , russisch Дмитрий Борисович Фукс , German Dmitri Borissowitsch Fuchs; born September 30, 1939 in Kazan , Russian SFSR ) is a Russian-American mathematician who deals in particular with the representation theory of infinite-dimensional love Groups and busy with topology.

life and work

Fuchs received his doctorate in 1964 under Albert S. Schwarz , later also a professor at the University of California, at Lomonossow University (candidate title), where he then taught. At that time, Schwarz led a seminar on algebraic topology with Michail Postnikow and Wladimir Boltjanski , and Fuchs published there with him as a student (as well as with Askold Winogradow and Boris Delone ). He completed his habilitation (Russian doctorate) in 1987 at the State University of Tbilisi . Since 1991 he has been a professor at the University of California, Davis .

With Israel Gelfand he introduced Gelfand-Fuchs cohomology of Lie algebras in 1970 . The theory has applications in the proof of some of the Macdonald identities in combinatorics and in the computation of characteristic classes of scrolls . With Boris Feigin , for example, he determined the structure of the Verma modules in the representation theory of Virasoro algebras , which have applications in string theory and conformal field theory .

His students include Boris Feigin, with whom he worked a lot, Fedor Malikow, Sergei Tabachnikov and Vladimir Rochlin as well as Edward Frenkel (he unofficially looked after him with Feigin).

In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( New results on the characteristic classes of foliations ).

Fonts

with Anatoli T. Fomenko , Viktor L. Gutenmacher: Homotopic topology. Akadémiai Kiadó, Budapest 1986, ISBN 963-05-3544-0 .
Cohomology of infinite-dimensional Lie algebras. Consultants Bureau, New York NY et al. 1986, ISBN 0-306-10990-5 .
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, ISBN 0-8218-4121-1 , pp. 65-74.
with Serge Tabachnikov: Mathematical omnibus. Thirty lectures on classic mathematics. American Mathematical Society, Providence RI 2007, ISBN 978-0-8218-4316-1 (In German: A graph of mathematics. 30 lectures on classical mathematics. Springer, Berlin et al. 2011, ISBN 978-3-642-12959-9 ).

literature

Alexander Astashkevich, Serge Tabachnikov (Eds.): Differential topology, infinite-dimensional lie algebras, and applications. DB Fuchs' 60th Anniversary Collection (= American Mathematical Society. Translations. Series 2, 194). American Mathematical Society, Providence RI 1999, ISBN 0-8218-2032-X .

Web links

Individual evidence

^ Entry on Dmitry Fuchs at Math-Net.Ru
↑ Great Biographical Encyclopedia (Russian)
↑ 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, doi : 10.1007 / BF01676621 . 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, doi : 10.1070 / IM1970v004n02ABEH000908 .
↑ 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, doi : 10.1007 / BF01077264 . Boris L. Feigin, Dmitry B. Fuchs: Representations of the Virasoro Algebra. In: Anatolii M. Vershik, Dmitrii P. Zhelobenko (ed.): Representation of Lie groups and related topics (= Advanced Studies in Contemporary Mathematics. Vol. 7). Gordon and Breach, New York NY et al. 1990, ISBN 2-88124-678-8 , pp. 465-554.
↑ Fuchs also lectured at the unofficial Jewish university in Moscow, the Institute for Oil and Gas. Mark Saul: Kerosinka: An Episode in the History of Soviet Mathematics. In: Notices of the American Mathematical Society. Vol. 46, No. 10, 1999, ISSN 0002-9920 , pp. 1217-1220, digital version (PDF; 72 kB) . Retrieved May 23, 2015.

personal data
SURNAME	Fuchs, Dmitry
ALTERNATIVE NAMES	Fuchs, Dmitry Borisovich; Fuks, DB; Фукс, Дмитрий Борисович (Russian); Fuchs, Dmitri Borissowitsch (German transcription)
BRIEF DESCRIPTION	Russian-American mathematician
DATE OF BIRTH	September 30, 1939
PLACE OF BIRTH	Kazan , Russian SFSR

[1] Entry on Dmitry Fuchs at Math-Net.Ru

[2] Great Biographical Encyclopedia (Russian)

[3] 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, doi : 10.1007 / BF01676621 . 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, doi : 10.1070 / IM1970v004n02ABEH000908 .

[4] 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, doi : 10.1007 / BF01077264 . Boris L. Feigin, Dmitry B. Fuchs: Representations of the Virasoro Algebra. In: Anatolii M. Vershik, Dmitrii P. Zhelobenko (ed.): Representation of Lie groups and related topics (= Advanced Studies in Contemporary Mathematics. Vol. 7). Gordon and Breach, New York NY et al. 1990, ISBN 2-88124-678-8 , pp. 465-554.

[5] Fuchs also lectured at the unofficial Jewish university in Moscow, the Institute for Oil and Gas. Mark Saul: Kerosinka: An Episode in the History of Soviet Mathematics. In: Notices of the American Mathematical Society. Vol. 46, No. 10, 1999, ISSN 0002-9920 , pp. 1217-1220, digital version (PDF; 72 kB) . Retrieved May 23, 2015.