Vladimir Drinfeld

Vladimir Drinfeld ( Ukrainian Володимир Гершонович Дрінфельд , Volodymyr Gerschonowitsch Drinfeld ; Russian Владимир Дринфельд ; born February 14, 1954 in Charkow ) is a Ukrainian mathematician who emigrated to the USA .

life and work

Vladimir Drinfeld was born in 1954 as the son of the Ukrainian-Jewish professor of mathematics at Kharkov University Gershon I. Drinfeld (1908–2000).

At the age of fifteen, Drinfeld represented the Soviet Union at the International Mathematical Olympiad in Bucharest in 1969 and won the gold medal there. Between 1969 and 1974 he studied mathematics at Lomonosov University in Moscow . After successfully completing the diploma, an aspirant course followed in 1977 . His candidate dissertation , with which he received his doctorate in 1978, was written under the guidance of Yuri Manin .

Since he could not get a suitable job in Moscow because of his Jewish descent, he went to the Autonomous Republic of Bashkiria to work as a mathematics teacher in the provincial capital Ufa at the Bashkir State University and at other universities in Ufa.

In 1981 he returned to Kharkov and finally found a job at the Werkin Institute for Low Temperature Physics and Engineering of the Ukrainian Academy of Sciences. He also taught at Kharkiv University.

In 1988 he completed his habilitation at the Steklow Institute in Moscow ( Russian doctorate ).

In 1990 he received the Fields Medal for his work on quantum groups and in number theory . In 1992 he was appointed a member of the Academy of Sciences of Ukraine .

In 1998 he emigrated to the USA and in December 1998 he became Distinguished Service Professor at the University of Chicago , where he works with Alexander Beilinson , among others .

His main areas of work are mathematical physics (for example, vertex algebras , in the book Chiral Algebras from 2004 with Alexander Beilinson), number theory and algebraic geometry . He is considered to be the great pioneer of the geometric Langlands conjecture (partly with Alexander Beilinson in the early 1990s).

His proof of the Langlands conjecture for the special case of the group GL ₂ over a function field over a finite field is groundbreaking in this area: He was the first result for a non- Abelian group in the global case. In connection with this proof, he introduced Drinfeld modules in 1973 , which he called elliptical modules (generalizations are the Chtoukas introduced by Drinfeld , named after Russian Штука after German Stück ).

From him and Yuri Manin the ADHM construction of comes Yang-Mills - instantons (regardless of Nigel Hitchin and Michael Atiyah found, the first letter of all four represent ADHM). In a lecture at the 1986 International Congress of Mathematicians in Berkeley , he introduced quantum groups (as did Michio Jimbō in Japan at the same time and independently ) and in 1978 he was invited speaker at the ICM in Helsinki ( Langlands conjecture for GL (2) over function fields ).

In 2008 he was admitted to the American Academy of Arts and Sciences and in 2016 to the National Academy of Sciences . In 2018 he received the Wolf Prize for Mathematics.

literature

• Yuri Manin : On the Mathematical Work of Vladimir Drinfeld in Ichirō Satake (ed.): Proceedings of the International Congress of Mathematicians, August 21-29, 1990, Kyoto, Japan , Springer, 1991 (English; laudation for Fields Medal 1990; online )

Fonts (selection)

• Эллиптические модули . In: Mat. Sb. (NS) . tape 94 (136) , no. 4 (8) , 1974, pp. 594–627 (Russian, online [PDF; 3.7 MB ]).
  • English translation: Elliptic Modules . In: Mathematics of the USSR-Sbornik . tape 23 , no. 4 , 1974, p. 561-592 , doi : 10.1070 / SM1974v023n04ABEH001731 .
• Elliptic modules. (Russian) Mat. Sb. (NS) 94 (136) (1974), 594-627, 656. Translated into Math. USSR-Sb. 23 (1974), no. 4, 561-592 (1976).
• Coverings of -adic symmetric domains. ${\displaystyle p}$(Russian) funcional. Anal. i Priložen. 1976, 10, no. 2, 29-40.
• with Atiyah, Hitchin, Manin: Construction of instantons. Phys. Lett. A 65 (1978) no. 3, 185-187.
• Langlands' conjecture for over functional fields. ${\displaystyle {\rm {GL}}(2)}$Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 565-574, Acad. Sci. Fennica, Helsinki, 1980.
• with Sokolov: Lie algebras and equations of Korteweg-de Vries type. (Russian) Current problems in mathematics, Vol. 24, 81-180, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984.
• Hopf algebras and the quantum Yang-Baxter equation. (Russian) Docl. Akad. Nauk SSSR 283 (1985) no. 5, 1060-1064.
• A new realization of Yangians and of quantum affine algebras. (Russian) Docl. Akad. Nauk SSSR 296 (1987) no. 1, 13-17; translated in Soviet Math. Dokl. 36 (1988) no. 2: 212-216
• Quantum groups. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 798-820, Amer. Math. Soc., Providence, RI, 1987.
• Almost cocommutative Hopf algebras. (Russian) Algebra i Analiz 1 (1989), no.2, 30--46; translated in Leningrad Math. J. 1 (1990), no. 2, 321–342
• Quasi-Hopf algebras. (Russian) Algebra i Analiz 1 (1989), no. 6, 114-148; translated in Leningrad Math. J. 1 (1990), no. 6, 1419-1457
• On quasitriangular quasi-Hopf algebras and on a group that is closely connected with . ${\displaystyle {Gal}({\overline {\mathbb {Q} }}/{\mathbb {Q} })}$(Russian) Algebra i Analiz 2 (1990), no. 4, 149-181; translated in Leningrad Math. J. 2 (1991), no. 4, 829-860.
• DG quotients of DG categories. J. Algebra 272 (2004), no. 2, 643-691.
• with Beilinson: Chiral algebras. American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004. ISBN 0-8218-3528-9
• with Beilinson: Quantization of Hitchin's integrable system and Hecke eigensheaves , Preprint 1991, pdf
• with Gelaki, Nikshych, Ostrik: On braided fusion categories. I. Selecta Math. (NS) 16 (2010), no. 1, 1-119.

Web links

• John J. O'Connor, Edmund F. Robertson :  Vladimir Drinfeld. In: MacTutor History of Mathematics archive .

Individual references and notes

1. ↑ The Russian-Soviet degree "candidate" corresponds to the German doctoral title and the English-American "Ph.D."