Efim Zelmanov

Efim Isaakovich Zelmanov (Russian: Ефи́м Исаа́кович Зе́льманов; born 7 September 1955 in Khabarovsk) is a Russian-American^[1] mathematician, known for his work on combinatorial problems in nonassociative algebra and group theory, including his solution of the restricted Burnside problem. He was awarded a Fields Medal at the International Congress of Mathematicians in Zürich in 1994.

Zelmanov was born into a Jewish family in Khabarovsk, Soviet Union (now in Russia). He entered Novosibirsk State University in 1972, when he was 17 years old.^[2] He obtained a doctoral degree at Novosibirsk State University in 1980, and a higher degree at Leningrad State University in 1985. He had a position in Novosibirsk until 1987, when he left the Soviet Union.

In 1990 he moved to the United States, becoming a professor at the University of Wisconsin–Madison. He was at the University of Chicago in 1994/5, then at Yale University. In 1996 he became a Distinguished Professor at the Korea Institute for Advanced Study and in 2002, he became a professor at the University of California, San Diego.^[3] In 2022, he moved to the People's Republic of China and joined the Southern University of Science and Technology in Shenzhen, China.^[4][5] He served as a chair professor and the scientific director of the SUSTech International Center for Mathematics.

Zelmanov was elected a member of the U.S. National Academy of Sciences in 2001,^[6] becoming, at the age of 47, the youngest member of the mathematics section of the academy.^[7] He is also an elected member of the American Academy of Arts and Sciences (1996)^[8] and a foreign member of the Korean Academy of Science and Engineering and of the Spanish Royal Academy of Sciences.^[9] In 2012 he became a fellow of the American Mathematical Society.^[10]

Zelmanov gave invited talks at the International Congress of Mathematicians in Warsaw (1983), Kyoto (1990) and Zurich (1994).^[11] He delivered the 2004 Turán Memorial Lectures.^[12] He was awarded Honorary Doctor degrees from the University of Hagen, Germany (1997),^[13] the University of Alberta, Canada (2011),^[14] Taras Shevchenko National University of Kyiv, Ukraine (2012),^[15] the Universidad Internacional Menéndez Pelayo in Santander, Spain (2015)^[16] and the University of Lincoln, UK (2016).^[17][18]

Zelmanov's early work was on Jordan algebras in the case of infinite dimensions. He was able to show that Glennie's identity in a certain sense generates all identities that hold. He then showed that the Engel identity for Lie algebras implies nilpotence, in the case of infinite dimensions.

Notable publications

• Zelʹmanov, E.I. Solution of the restricted Burnside problem for groups of odd exponent. Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 1, 42–59, 221. English translation in Math. USSR-Izv. 36 (1991), no. 1, 41–60. doi:10.1070/IM1991v036n01ABEH001946
• Zelʹmanov, E.I. Solution of the restricted Burnside problem for 2-groups. Mat. Sb. 182 (1991), no. 4, 568–592. English translation in Math. USSR-Sb. 72 (1992), no. 2, 543–565. doi:10.1070/SM1992v072n02ABEH001272

References

External links

• Efim Zelmanov at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Efim Zelmanov", MacTutor History of Mathematics Archive, University of St Andrews
• The Work of Efim Zelmanov (Fields Medal 1994) by Kapil Hari Paranjape.