Efim Zelmanov

Efim Zelmanov is the the Rita L. Atkinson Professor of Mathematics at the University of California, San Diego. He is also a Distinguished Professor at the Korea Institute for Advanced Study. He is a member of the National Academy of Sciences. Zelmanov's Ph.D. thesis (1980) on nonassociative algebra completely changed the whole subject area of Jordan algebras by extending results from the classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras. 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. His work on Jordan algebras and Lie algebras would have guaranteed Zelmanov a place as one of the great algebraists of the 20th century. In 1991, however, 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 by solving the restricted Burnside problem. In 1994 Zelmanov was awarded the Fields Medal for this work at the International Congress of Mathematicians in Zurich. He has received honorary doctorates from the Queen's University of Belfast, Northern Ireland, the University of Alberta in Canada, the University of Oviedo in Spain, and the University of Hagen in Germany.