Boris Lvovich Feigin

Boris Lwowitsch Feigin ( Russian Борис Львович Фейгин ; English transcription Boris Lvovich Feigin; born November 20, 1953 ) is a Russian mathematician who deals with representation theory of infinite-dimensional Lie algebras .

Life

Feigin graduated from Lomonosov University in 1975 with Dmitry Fuchs (Characteristic Classes of Flags of Leaves). Before that he had also studied with Israel Gelfand and AL Onishchik. For political reasons and because he was Jewish, he was not allowed to study for a doctorate. He worked as a programmer in industry (which, years later, earned him an income from the proceeds of the programs he wrote), but thanks to the influence of friends he was able to do his doctorate at the Demidow State University in Yaroslavl and was at in the 1980s Institute for Solid State Physics in Chernogolowka . Since the 1990s he has been a professor at the Independent University in Moscow. Among other things, he was visiting scholar at IHES . Currently (2009) he is also at the Steklow Institute , the Landau Institute and the École polytechnique (Palaiseau) in Paris.

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He first dealt with the cohomology of infinite-dimensional Lie algebras, which initially came from geometric applications (such as Lie algebra-valued functions on the circle). Later he dealt with the representation of infinite-dimensional Lie algebras from the field of mathematical physics, which became important in string theory from the late 1960s ( Virasoro algebras , Kac-Moody algebras ). The work provided important techniques in conformal field theory and the geometric Langlands program (developed by Frenkel and others). He worked with his teacher Fuchs and his student Frenkel ( Wakimoto modules ). With Boris Tsygan (who discovered cyclic cohomology independently of Alain Connes ) he dealt early with non-commutative geometry .

Feigin also gave an early mathematical formulation of the BRST method (Becchi, Rouet, Stora), which he called semi-infinite homology . In 1990 he gave a plenary lecture at the ICM in Kyōto (Conformal Field Theory and Cohomologies of the Lie Algebra of Holomorphic Vector Fields on a Complex Curve).

Edward Frenkel is one of his PhD students . His son Eugene Feigin is also a mathematician and published with Boris Feigin.

Web links

Remarks

↑ From the end of the 1960s there was a new wave of obstacles that were placed in the way of Jewish and politically unpopular academics, partly due to the first signs of opposition in the Soviet Union from the mid-1960s, including those of mathematicians in the Lomonosov University was supported. As a result, no Jewish mathematicians were admitted to extended studies there, and none were newly hired. The same was true of the Steklow Institute. Jewish mathematicians had to study at other universities and then worked on mathematical problems in institutes in the energy sector. Before that, there was a major wave of anti-Semitic measures at universities from the end of World War II until the mid-1950s.
↑ Alexander Belavin tells in his memories of Feigin in the Moscow Mathematics Journal that conversations with Feigin were important for the development of the fundamental work of Belavin, Alexander Zamolodchikov , Polyakov on conformal field theory 1984.

personal data
SURNAME	Feigin, Boris Lvovich
ALTERNATIVE NAMES	Фейгин, Борис Львович (Russian spelling); Feigin, Boris Lvovich (English transcription)
BRIEF DESCRIPTION	Russian mathematician
DATE OF BIRTH	November 20, 1953

[1] From the end of the 1960s there was a new wave of obstacles that were placed in the way of Jewish and politically unpopular academics, partly due to the first signs of opposition in the Soviet Union from the mid-1960s, including those of mathematicians in the Lomonosov University was supported. As a result, no Jewish mathematicians were admitted to extended studies there, and none were newly hired. The same was true of the Steklow Institute. Jewish mathematicians had to study at other universities and then worked on mathematical problems in institutes in the energy sector. Before that, there was a major wave of anti-Semitic measures at universities from the end of World War II until the mid-1950s.

[2] Alexander Belavin tells in his memories of Feigin in the Moscow Mathematics Journal that conversations with Feigin were important for the development of the fundamental work of Belavin, Alexander Zamolodchikov , Polyakov on conformal field theory 1984.