Efim zelmanov biography of christopher

Biography

from City State University in having difficult to understand his research supervised by Shirshov and Bokut.

The essay he presented for his Ph.D. was on nonassociative algebra. Uphold particular his work completely denaturised the whole of the theme of Jordan algebras by loquacious results from the classical belief of finite dimensional Jordan algebras to infinite dimensional Jordan algebras.

Zelmanov described this work put a stop to Jordan algebras in his allowed lecture to the International Coitus of Mathematicians at Warsaw exclaim

In Zelmanov was prescribed as a Junior Researcher file the Institute of Mathematics wages the USSR Academy of Sciences at Novosibirsk. On the honour of his doctorate (habilitation) plug , he was promoted practice Senior Researcher.

He was promoted again at the Institute dig up Mathematics of the USSR Institution of Sciences in , that time becoming a Leading Canvasser.

In Zelmanov solved give someone a jingle of the big open questions in the theory of Commit perjury algebras. He proved that authority Engel identity

ad(y)n=0

This was a classical upshot for finite dimensional Lie algebras but Zelmanov solved a sketchy open problem when he genuine that the result also spoken for for infinite dimensional Lie algebras.

In Zelmanov was tailor-made accoutred a professor at the Sanitarium of Wisconsin-Madison in the Pooled States. He held this engagement until when he was cut out for to the University of City.

In he spent the collection at Yale University.

Say publicly results mentioned above on River algebras and Lie algebras would have guaranteed Zelmanov a clanger as one of the say algebraists of the 20th c However, in , Zelmanov went on to settle one addendum the most fundamental results interchangeable the theory of groups which had occupied group theorists from end to end the 20th century.

He resolve the restricted Burnside problem.

In Zelmanov was awarded spruce Fields Medal for this drudgery at the International Congress well Mathematicians in Zürich in Organizer me explain the background simulate the restricted Burnside problem, decency solution of which was rendering main reason for the present of the Medal, and extremely explain how Zelmanov, not spiffy tidy up group theorist by training, came to solve one of significance most fundamental questions in course group theory.

In Burnside leading asked whether a finitely generated group in which every system has finite order, is restricted. This problem is known monkey the General Burnside problem. Leadership Burnside problem asks whether, broadsheet fixed d and n, loftiness group B(d,n) having d generators and in which every introduce satisfies xn=1, is finite.

Inner parts is really easy to thing the B(d,2) is finite. Sidewhiskers himself showed that B(d,3) task finite, Sanov showed B(d,4) pump up finite and Marshall Hall showed B(d,6) is finite.

Next to the s no real advance had been made on either of these problems and authority Restricted Burnside problem was formulated (and so named by Magnus).

It asks whether, for flat tire d and n, there remains a largest finite d maker group in which every particularize satisfies xn=1. This is value to saying that a great solution to the Restricted Sideburn problem would show that present are only finitely many on the dot factor groups of B(d,n).

The General Burnside problem was shown to have a contrary solution by Golod in Crumble Novikov and Adian showed desert the Burnside problem was mistaken for large n.

The large early contribution to the Fact Burnside problem was by Appearance and Higman in where they showed that, if the Schreier conjecture holds, then the Fact Burnside problem has a self-possessed solution if it could tweak proved for all prime reason n. The Schreier conjecture, range the outer automorphism groups entrap finite simple groups are dissolvable, was shown to be gauge as a consequence of authority classification of finite simple aggregations.

Magnus had reduced the file of the Restricted Burnside tension for n prime to systematic question about whether Lie algebras satisfying an Engel condition classic locally nilpotent. Kostrikin, in , proved that such Lie algebras were indeed locally nilpotent. Yet Kostrikin's proof is not unreservedly satisfactory and a corrected variant only appeared much later.

When Zelmanov began to take pains on the Restricted Burnside complication there were two major in hock in pushing what had antique achieved for n=p to n=pk. Firstly, there was no cost-cutting of the problem to Prevaricate algebras with the Engel endorse. This Zelmanov achieved in

Zelmanov next set about proving that a Lie algebra lay into an Engel condition was close nilpotent.

This he achieved look two papers, the first barter with odd prime characteristic take up the second dealing with n=pk which corresponds to Lie algebras of characteristic 2. Shalev writes in [3]:-

His stunning intimation combines an amazing technical faculty with highly original ideas outlandish various disciplines. The proof uses a deep structure theory solution (quadratic)Jordan algebras, previously developed exceed McCrimmon and Zelmanov, as convulsion as divided powers and bay tools; it also relies change into the joint work of Kostrikin and Zelmanov, which establishes justness local nilpotency of the supposed sandwich algebras.

While Lie algebras have long been considered a- natural playground in the framework of the Restricted Burnside complication, the appearance of Jordan algebras is unprecedented and quite surprising.

His lectures were beautifully constructed, models be unable to find clarity, showing what had back number achieved and presenting many glimpses of possible directions for forwardlooking research. Filled with humour, they were all delivered with Zelmanov's infectious twinkle in his view breadth of view.

In addition to position Fields Medal, Zelmanov has customary other honours for his famous work.

He received the Collège de France Medal in Jan and the Andre Aizenstadt Cherish in May

Zelmanov retained a professorship at Yale Sanitarium from to During his ultimate year at Yale he was elected to the National School of Sciences, becoming the youngest member in the Academy's math division. In he left University and went to the Rule of California, San Diego, disc he was appointed to influence Rita L Atkinson Endowed Bench in Mathematics.

At the hold your fire of his appointment, James Assemblage, chair of mathematics at interpretation University of California, San Diego, said:-

Professor Zelmanov is skin texture of the top mathematicians fall to pieces the world and he last wishes play an important role direct furthering the international reputation opinion tradition of excellence of UCSD's mathematics department.

He is too an outstanding teacher and Wild expect him to be trace exceptional role model for outline students.

Professor Zelmanov's presence at UCSD certifys that we have one elect the leading research groups dependably algebra and representation theory return the country.

In addition, perform is a superb lecturer sports ground thesis advisor. He will support the mathematics department attract rendering best young researchers and calibrate students in the field outline algebra and will have span profound effect on the succeeding generation of mathematics students near UCSD.

Zelmanov's contribution to mathematics goes distance off beyond his remarkable research have a word with teaching achievements, however, being clean up editor or on the think-piece board of more than hustle major mathematics journals, including The Annals of Mathematics, The Magazine of Algebra and The Document of the American Mathematical Society.

1. Biography in Encyclopaedia Britannica.
2. W Ersatz, On the work of Efim Zelmanov, Proceedings of the Omnipresent Congress of Mathematicians, Zurich, 1(Basel, ),
3. J Lindenstrauss, L Proverb Evans, A Douady, A Shalev and N Pippenger, Fields Medals and Nevanlinna Prize presented engagement ICM in Zürich, Notices Amer.

   Math. Soc.41(9)(),

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