Efim Zelmanov

Efim Zelmanov 2006

Efim zelmanov (actually Russian Ефим Исаакович Зельманов Yefim Isaakowitsch Selmanow , scientific. Transliteration Efim Isaakovič Zel'manov * 7. September 1955 in Khabarovsk ) is a Russian mathematician who is primarily concerned with algebra employed (non-associative algebra, group theory) and Was awarded the Fields Medal in 1994.

Career

Zelmanov studied at the Novosibirsk State University , graduating in 1977. He then began to teach at the same university and continue his own research. In 1981 he did his doctorate with Leonid Bokut with a thesis on Jordan algebras of infinite dimensions.

In 1980, Zelmanov was appointed junior scientist at the Novosibirsk Institute of Mathematics of the Academy of Sciences of the USSR . He completed his habilitation in 1985 and was promoted to full-time researcher in 1986. In 1990 he went to the USA and became a professor at the University of Wisconsin-Madison . In 1994 he went to the University of Chicago and the following year to Yale University . In 1996 he was founding director of the School of Mathematics of the Korea Institute for Advanced Study in Seoul . He is currently (2013) Professor at the University of California at San Diego and Distinguished Professor at the Korea Institute for Advanced Study.

research

Zelmanov is best known for his solution to the “restricted Burnside problem ” in group theory . The “classic Burnside problem” asks whether finitely generated groups , whose all elements have finite order , are finite. The "restricted Burnside problem" asks whether there are finitely many finite groups G that are finitely generated ( m generators) and whose elements have order n (more precisely, according to a bound for the order of G , depending only on n , m asked). This problem was formulated in the 1930s and already dealt with for prime n by Alexei Kostrikin in the 1950s. Zelmanov solves the problem for any n . He showed that there is such a barrier.

Prices and memberships

In addition to the Fields Medal , Zelmanov received the Collège de France medal in 1991 and the André Aisenstadt Prize in May 1996 for his outstanding achievements in mathematics . In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw ( On the theory of Jordan algebras ) and in 1990 in Kyoto ( On the restricted Burnside problem ). He is a Fellow of the American Mathematical Society and the American Academy of Arts and Sciences (1997) and a member of the National Academy of Sciences (2001). He is also a member of the European Academy of Sciences (2003), the Royal Spanish Academy of Sciences (2001) and the Korean Academy of Science and Technology (2008). He has multiple honorary doctorates (University of Hagen, University of Oviedo, University of Alberta, Queen * s University Belfast).

In 2007/08 and 2008/09 he was on the Abel Prize Committee.

Works (selection)

• Prime Jordan algebras. Sibirsk. Mat. Zh. 1983, 24, 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: no.2: 543-565 (1992)
• On periodic compact groups. Israel J. Math. 77 (1992), no. 1-2, 83-95.
• Nile 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 superalgebras with semisimple even part. J. Algebra 270 (2003), no. 2, 374-444.

Web links

• John J. O'Connor, Edmund F. Robertson :  Efim Zelmanov. In: MacTutor History of Mathematics archive .
• Walter Feit: On the work of Efim Zelmanov . (PDF)
• Website at KIAS
• Videos by and about Efim Zelmanov in the AV portal of the Technical Information Library

Individual evidence

1. ↑ Efim Zelmanov in the Mathematics Genealogy Project (English)