Efim Zelmanov

Efim Zelmanov (actually Russian Ефим Исаакович Зельманов / Yefim Isaakowitsch Selmanow, scientific transliteration Efim Isaakovič Zel'manov; born September 7, 1955 in Khabarovsk ) is a Russian mathematician of Jewish descent, especially with algebra dealt ( non- associative algebras, group theory ) and in 1994 was awarded the Fields medal.

Career

Zelmanov studied at the State University in Novosibirsk, he received his diploma in 1977. Afterwards, he began to teach and continue his own research at the same university. In 1981 he received his doctorate with Leonid Bokut with the work on Jordan algebras of infinite dimension.

1980 Zelmanov junior scientists was appointed on the Novosibirsk Institute of Mathematics of the Academy of Sciences of the USSR. In 1985 he qualified as a professor and in 1986 was promoted to full-time researchers. In 1990 he went to the USA and he became a professor at the University of Wisconsin - Madison. In 1994 he went to the University of Chicago and the following year at Yale University. In 1996 he was the founding director of the " School of Mathematics " of the Korea Institute for Advanced Study in Seoul. Currently (2013 ) he is a professor at the University of California in San Diego and Distinguished Professor at the Korea Institute for Advanced Study.

Research

Zelmanov is mainly known for his solution to the " restricted Burnside problem" in group theory. The "classical Burnside problem" asks whether finitely generated groups, all of whose elements have finite order, finite. The "restricted Burnside problem," according to whether a finite number of finite groups are G, the finitely generated (m generators) and whose elements are of order n asks (to be more precise, after a bound on the order of G, depending only on n, m asked ). This problem was formulated in the 1930s and treated for prime n already Alexei Kostrikin in the 1950s. Zelmanov solve the problem for arbitrary n He showed that there is such a barrier.

Prices

For his outstanding achievements in mathematics Zelmanov won both the Fields Medal in January 1992 the French Collège de medal and in May 1996 the André Aisenstadt price. In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw ( On the theory of Jordan algebras ) and 1990 in Kyoto ( On the restricted Burnside problem). He is a Fellow of the American Mathematical Society.

Works (selection)

• Prime Jordan algebras. Sibirsk. Mat Zh. 24 (1983 ), no 1, 89-104
• With K. McCrimmon: The structure of 'strongly prime quadratic Jordan algebras. Adv in Math 69 (1988 ), no 2, 133-222.
• Solution of the restricted Burnside problem- for groups of odd exponent. Russian: Izv. Akad Nauk SSSR Ser. Mat 54 (1990 ), no 1, 42-59, 221; English translation: Math USSR- Izv. 36 (1991 ), no 1, 41-60
• Solution of the restricted Burnside problem- for 2 -groups. Russian: Mat Sb 182 (1991), no 4, 568-592; English translation: Math USSR- Sb. 72 (1992 ), no 2, 543-565
• On periodic compact groups. Israel J. Math 77 (1992 ), no 1-2, 83-95.
• Nil rings and periodic groups. With a foreword by Jongsik Kim. KMS Lecture Notes in Mathematics. Korean Mathematical Society, Seoul, 1992. X 79 pp.
• With G. Benkart: Lie algebras graded by finite root systems and intersection matrix algebras. Invent. Math 126 (1996), no 1, 1-45.
• With ML Racine: Simple Jordan algebras with super semisimple even part. J. Algebra 270 (2003), no 2, 374-444.