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CRM - University of Ottawa Distinguished Lecture Series

TITLE:Asymptotic properties of finite groups and finite dimensional algebras
SPEAKER:Efim Zelmanov (University of California, San Diego)
DATE:Vendredi, 19 Septembre 2008
TIME:3:30 pm
ROOM:B5
ABSTRACT:

We will discuss the limits of finite groups and finite dimensional algebras and their connections with number theory, low dimensional topology, combinatorics etc.

Video of the conference: Part 1, Part 2, Part 3 and Part 4; and slides of the conference

About the speaker Efim Zelmanov is world-famous for his work on combinatorial problems in nonassociative algebra and group theory, most importantly his solution of the restricted Burnside problem.

He obtained his doctoral degree at Novosibirsk State University in 1980 under the supervision of Shirshov and Bokut. His thesis completely changed the subject of Jordan algebras by extending results of the classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras. He described this work in an invited lecture at the ICM Warsaw in 1983. In 1987 Zelmanov solved one of the big open questions in the theory of Lie algebras. He proved that the Engel identity ad(y)n = 0 implies that the algebra is necessarily nilpotent. This was a classical result for finite dimensional Lie algebras but Zelmanov was able to show that the result also held for infinite dimensional Lie algebras.

In 1990 he moved to the United States. Since 2002 he has been a professor at the University of California, San Diego. The results mentioned above on Jordan algebras and Lie algebras would have guaranteed Zelmanov a place as one of the great algebraists of the 20th century. However, in 1991, Zelmanov went on to settle one of the most fundamental results in the theory of groups which had occupied group theorists throughout the 20th century: He solved the restricted Burnside problem! He was awarded a Fields Medal at the International Congress of Mathematicians in Zürich in 1994. Among his many other awards are the Collège de France Medal in January 1992 and the André Aizenstadt Prize in May 1996.