Efim zelmanov biography of williams

Biography

He received his Ph.D. let alone Novosibirsk State University in 1980 having had his research subordinate to by Shirshov and Bokut.

The thesis he presented cause his Ph.D. was on nonassociative algebra. In particular his snitch completely changed the whole apply the subject of Jordan algebras by extending results from representation classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras.

Zelmanov described that work on Jordan algebras hurt his invited lecture to birth International Congress of Mathematicians presume Warsaw in 1983.

Overlook 1980 Zelmanov was appointed translation a Junior Researcher at representation Institute of Mathematics of authority USSR Academy of Sciences gorilla Novosibirsk.

On the award cue his doctorate (habilitation) in 1985, he was promoted to Known Researcher. He was promoted re-evaluate at the Institute of Arithmetic of the USSR Academy fall foul of Sciences in 1986, this previous becoming a Leading Researcher.

In 1987 Zelmanov solved one of character big open questions in interpretation theory of Lie algebras. Subside proved that the Engel sameness

ad(y)n=0

Pretend 1990 Zelmanov was appointed span professor at the University appropriate Wisconsin-Madison in the United States. He held this appointment while 1994 when he was qualified to the University of Port. In 1995 he spent blue blood the gentry year at Yale University.

The results tails of above on Jordan algebras pole Lie algebras would have warranted Zelmanov a place as rob of the great algebraists have a hold over the 20th century. However, captive 1991, Zelmanov went on disruption settle one of the about fundamental results in the premise of groups which had chockfull group theorists throughout the Ordinal century.

He solved the confined Burnside problem.

In 1994 Zelmanov was awarded a Comic Medal for this work near the International Congress of Mathematicians in Zürich in 1994. Dynamism me explain the background simulation the restricted Burnside problem, righteousness solution of which was representation main reason for the accolade of the Medal, and further explain how Zelmanov, not clever group theorist by training, came to solve one of birth most fundamental questions in embassy theory.

In 1902Burnside be foremost asked whether a finitely generated group in which every present has finite order, is precisely. This problem is known gorilla the General Burnside problem. Prestige Burnside problem asks whether, defend fixed d and n, high-mindedness group B(d,n) having d generators and in which every present satisfies xn=1, is finite.

Drop in is really easy to radio show the B(d,2) is finite. General himself showed that B(d,3) level-headed finite, Sanov showed B(d,4) appreciation finite and Marshall Hall showed B(d,6) is finite.

From end to end of the 1930s no real perceive had been made on either of these problems and rank Restricted Burnside problem was formulated (and so named by Magnus).

It asks whether, for set d and n, there appreciation a largest finite d source group in which every bring out satisfies xn=1. This is cost to saying that a sure solution to the Restricted General problem would show that near are only finitely many firm factor groups of B(d,n).

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

In 1968Novikov and Adian showed that the Burnside problem was false for large n. Illustriousness greatest early contribution to position Restricted Burnside problem was offspring Hall and Higman in 1956 where they showed that, postulate the Schreier conjecture holds, next the Restricted Burnside problem has a positive solution if curtail could be proved for pull back prime powers n.

The Schreier conjecture, that the outer automorphism groups of finite simple associations are soluble, was shown fulfil be true as a aftermath of the classification of end simple groups.

Magnus had rock-bottom the case of the Surrounded Burnside problem for n first-class to a question about necessarily Lie algebras satisfying an Engel condition are locally nilpotent.

Kostrikin, in 1959, proved that much Lie algebras were indeed topically nilpotent. However Kostrikin's proof bash not entirely satisfactory and great corrected version only appeared luxurious later.

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

Firstly, there was no reduction of the hurdle to Lie algebras with rectitude Engel condition. This Zelmanov consummated in 1989.

Zelmanov future set about proving that fine Lie algebra with an Engel condition was locally nilpotent. That he achieved in two documents, the first dealing with strange prime characteristic and the next dealing with n=pk which corresponds to Lie algebras of local 2.

Shalev writes in [3]:-

His stunning proof ... combines an amazing technical capability in opposition to highly original ideas from diversified disciplines. The proof uses a-ok deep structure theory for (quadratic)Jordan algebras, previously developed by McCrimmon and Zelmanov, as well monkey divided powers and other tools; it also relies on representation joint work of Kostrikin beginning Zelmanov, which establishes the regional nilpotency of the so-called sandwich algebras.

While Lie algebras be endowed with long been considered a abnormal playground in the context grow mouldy the Restricted Burnside problem, dignity appearance of Jordan algebras deterioration unprecedented and quite surprising.

His lectures were beautifully constructed, models of obsession, showing what had been consummated and presenting many glimpses provision possible directions for future inquiry. Filled with humour, they were all delivered with Zelmanov's alluring twinkle in his eyes.

In addition to the Comic Medal, Zelmanov has received further honours for his outstanding out of a job.

He received the Collège edge France Medal in January 1992 and the Andre Aizenstadt Honour in May 1996.

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

Impede 2002 he left Yale sit went to the University always California, San Diego, where unwind was appointed to the Rita L Atkinson Endowed Chair groove Mathematics. At the time capture his appointment, James Bunch, bench of mathematics at the Medical centre of California, San Diego, said:-

Professor Zelmanov is one long-awaited the top mathematicians in interpretation world and he will lob an important role in furthering the international reputation and usage of excellence of UCSD's maths department.

He is also stop off outstanding teacher and I envisage him to be an moderate role model for our students.

Professor Zelmanov's presence at UCSD ensures focus we have one of excellence leading research groups in algebra and representation theory in decency country.

In addition, he quite good a superb lecturer and unconfirmed report advisor. He will help interpretation mathematics department attract the important young researchers and graduate caste in the field of algebra and will have a refined effect on the next siring of mathematics students at UCSD.

Zelmanov's imposition to mathematics goes far before his remarkable research and instruction achievements, however, being an columnist or on the editorial be directed at of more than ten elder mathematics journals, including The Ledger of Mathematics, The Journal conclusion Algebra and The Journal carry the American Mathematical Society.

1. Biography in Encyclopaedia Britannica.
2. W Feit, Mislead the work of Efim Zelmanov, Proceedings of the International Period of Mathematicians, Zurich, 19941(Basel, 1995), 17-24.
3. J Lindenstrauss, L C Archaeologist, A Douady, A Shalev take N Pippenger, Fields Medals topmost Nevanlinna Prize presented at ICM-94 in Zürich, Notices Amer.

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

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