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 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. As of 2011, he is a professor at the University of California, San Diego^[3] and a Distinguished Professor at the Korea Institute for Advanced Study.

Zelmanov was elected a member of the U.S. National Academy of Sciences in 2001,^[4] becoming, at the age of 47, the youngest member of the mathematics section of the academy.^[5] He is also an elected member of the American Academy of Arts and Sciences (1996)^[6] and a foreign member of the Korean Academy of Science and Engineering and of the Spanish Royal Academy of Sciences.^[7] In 2012 he became a fellow of the American Mathematical Society.^[8]

Zelmanov gave invited talks at the International Congress of Mathematicians in Warsaw (1983), Kyoto (1990) and Zurich (1994).^[9] He was awarded Honorary Doctor degrees from the University of Alberta, Canada (2011),^[10] Shevchenko National University of Kyiv, Ukraine (2012),^[11] the Universidad Internacional Menéndez Pelayo in Santander, Spain (2015)^[12] and the University of Lincoln, UK (2016).^[13][14]

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.

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.