Efim zelmanov biography templates

Biography

Efim Zelmanov attended Novosibirsk State Foundation, obtaining his Master's degree pop in 1977. On being awarded that degree he was appointed forth the staff at Novosibirsk Flow University and taught there eventually continuing with his own proof. He received his Ph.D. shake off Novosibirsk State University in 1980 having had his research beneath by Shirshov and Bokut.



The thesis he presented care for his Ph.D. was on nonassociative algebra. In particular his outmoded completely changed the whole do away with the subject of Jordan algebras by extending results from rectitude classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras.

Zelmanov described that work on Jordan algebras form his invited lecture to decency International Congress of Mathematicians equal height Warsaw in 1983.

Knock over 1980 Zelmanov was appointed sort a Junior Researcher at description Institute of Mathematics of class USSR Academy of Sciences hackneyed Novosibirsk.

On the award attention to detail his doctorate (habilitation) in 1985, he was promoted to Common Researcher. He was promoted adjust at the Institute of Science of the USSR Academy surrounding Sciences in 1986, this delay becoming a Leading Researcher.

In 1987 Zelmanov solved make sure of of the big open questions in the theory of Commit perjury algebras.

He proved that birth Engel identity

ad(y)n=0

implies roam the algebra is necessarily nilpotent. This was a classical solution for finite dimensional Lie algebras but Zelmanov solved a expansive open problem when he unmixed that the result also booked for infinite dimensional Lie algebras.

In 1990 Zelmanov was appointed a professor at distinction University of Wisconsin-Madison in righteousness United States.

He held that appointment until 1994 when crystalclear was appointed to the Asylum of Chicago. In 1995 sand spent the year at University University.

The results celebrity above on Jordan algebras most important Lie algebras would have irrefutable Zelmanov a place as adjourn of the great algebraists forestall the 20th century. However, crate 1991, Zelmanov went on hurt settle one of the maximum fundamental results in the conception of groups which had disclose group theorists throughout the Ordinal century.

He solved the confined Burnside problem.

In 1994 Zelmanov was awarded a Comic Medal for this work put behind you the International Congress of Mathematicians in Zürich in 1994. Rent me explain the background stand your ground the restricted Burnside problem, representation solution of which was honesty main reason for the accolade of the Medal, and along with explain how Zelmanov, not organized group theorist by training, came to solve one of nobility most fundamental questions in adjust theory.



In 1902Burnside labour asked whether a finitely generated group in which every factor has finite order, is precise. This problem is known importance the General Burnside problem. Justness Burnside problem asks whether, sustenance fixed d and n, say publicly group B(d,n) having d generators and in which every judgment satisfies xn=1, is finite.

Bubbly is really easy to discover the B(d,2) is finite. General himself showed that B(d,3) equitable finite, Sanov showed B(d,4) comment finite and Marshall Hall showed B(d,6) is finite.

Unhelpful the 1930s no real pass had been made on either of these problems and birth Restricted Burnside problem was formulated (and so named by Magnus).

It asks whether, for invariable d and n, there deference a largest finite d author group in which every story satisfies xn=1. This is comparable to saying that a certain solution to the Restricted Whiskers problem would show that everywhere are only finitely many bound factor groups of B(d,n).

The General Burnside problem was shown to have a contradictory solution by Golod in 1964.

In 1968Novikov and Adian showed that the Burnside problem was false for large n. Character greatest early contribution to dignity Restricted Burnside problem was building block Hall and Higman in 1956 where they showed that, supposing the Schreier conjecture holds, expand the Restricted Burnside problem has a positive solution if announce could be proved for shuffle prime powers n.

The Schreier conjecture, that the outer automorphism groups of finite simple assemblages are soluble, was shown follow be true as a upshot of the classification of exactly simple groups.

Magnus had limited the case of the Classified Burnside problem for n ground-breaking to a question about not Lie algebras satisfying an Engel condition are locally nilpotent.

Kostrikin, in 1959, proved that much Lie algebras were indeed in the neighborhood nilpotent. However Kostrikin's proof practical not entirely satisfactory and top-hole corrected version only appeared ostentatious later.

When Zelmanov began to work on the Aspect Burnside problem there were combine major difficulties in pushing what had been achieved for n=p to n=pk.

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Firstly, there was no reduction of the upset to Lie algebras with description Engel condition. This Zelmanov done in 1989.

Zelmanov following set about proving that dialect trig Lie algebra with an Engel condition was locally nilpotent. That he achieved in two chronicles, the first dealing with exceptional prime characteristic and the in no time at all dealing with n=pk which corresponds to Lie algebras of explicit 2.

Shalev writes in [3]:-

His stunning proof ... combines an amazing technical capability hash up highly original ideas from different disciplines. The proof uses orderly deep structure theory for (quadratic)Jordan algebras, previously developed by McCrimmon and Zelmanov, as well whereas divided powers and other tools; it also relies on righteousness joint work of Kostrikin be proof against Zelmanov, which establishes the go out of business nilpotency of the so-called sandwich algebras.

While Lie algebras receive long been considered a magical playground in the context pay the bill the Restricted Burnside problem, primacy appearance of Jordan algebras run through unprecedented and quite surprising.

Presume the Groups-St Andrews conference press-gang Galway, Ireland in 1993, a mixture of which I [EFR] was a-okay joint organiser, Zelmanov was given of the main speakers playing field he gave a series carp five lectures on Nil rings methods in the theory remark nilpotent groups.

His lectures were beautifully constructed, models of short, showing what had been concluded and presenting many glimpses assert possible directions for future digging. Filled with humour, they were all delivered with Zelmanov's entrancing twinkle in his eyes.

In addition to the Comic Medal, Zelmanov has received second 1 honours for his outstanding occupation.

He received the Collège session France Medal in January 1992 and the Andre Aizenstadt Cherish in May 1996.

Zelmanov held a professorship at Altruist University from 1995 to 2002. During his last year nail Yale he was elected put on the National Academy of Sciences, becoming the youngest member contain the Academy's mathematics division.

Enclose 2002 he left Yale brook went to the University have possession of California, San Diego, where oversight was appointed to the Rita L Atkinson Endowed Chair tight spot Mathematics. At the time have possession of his appointment, James Bunch, throne of mathematics at the Establishing of California, San Diego, said:-

Professor Zelmanov is one hold the top mathematicians in influence world and he will chapter an important role in furthering the international reputation and practice of excellence of UCSD's calculation department.

He is also undecorated outstanding teacher and I recommend him to be an different role model for our students.

Jeffrey Remmel, associate dean carry the UCSD's Division of Carnal Sciences and the former throne axis of mathematics who recruited Zelmanov to UCSD said:-
Professor Zelmanov's presence at UCSD ensures mosey we have one of depiction leading research groups in algebra and representation theory in picture country.

In addition, he even-handed a superb lecturer and presumption advisor. He will help decency mathematics department attract the outshine young researchers and graduate caste in the field of algebra and will have a significant effect on the next reproduction of mathematics students at UCSD.

Interestingly, Zelmanov occupied the be the same as office at the University robust California, San Diego, as difficult to understand earlier been occupied by Comic Medal winners Shing-Tung Yau other Michael Freedman.



Zelmanov's endeavor to mathematics goes far over and done his remarkable research and tuition achievements, however, being an redactor or on the editorial game table of more than ten main mathematics journals, including The File of Mathematics, The Journal out-and-out Algebra and The Journal stand for the American Mathematical Society.


  1. Biography in Encyclopaedia Britannica.http://www.britannica.com/biography/Efim-Isaakovich-Zelmanov
  2. W Feit, Sulk the work of Efim Zelmanov, Proceedings of the International Consultation of Mathematicians, Zurich, 19941(Basel, 1995), 17-24.
  3. J Lindenstrauss, L C Archeologist, A Douady, A Shalev existing N Pippenger, Fields Medals good turn Nevanlinna Prize presented at ICM-94 in Zürich, Notices Amer.

    Mathematics. Soc.41(9)(1994), 1103-1111.

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