Harald Bohr foredrag med Efim Zelmanov

Titlen på Zelmanovs foredrag er ”Some open questions on asymptotics of groups and algebras”. Han skriver i sit resume:

”We will discuss open problems related to residually finite groups and infinite dimensional algebras. As is typical in Combinatorial Group Theory the problems will be inspired by (i) The Burnside Problem, (ii) growth, (iii) presentations by generators and relations.”

Professor Efim Zelmanov er en af vor tids mest fremtrædende matematikere. Han er modtager af Fields Medaljen i 1994 som anerkendelse af hans banebrydende arbejde indenfor abstrakt algebra, herunder gruppeteori, og specielt for hans løsning af det såkaldte Restricted Burnside Problem. Udover Fields Medaljen har professor Zelmanov modtaget andre æresbevisninger for hans fremragende arbejde, herunder Collège de France Medal (1992) og André Aizenstadt Prize (1996).

Efim Zelmanov studerede matematik ved State University i Novosibirsk, Rusland. Da han havde færdiggjort sin ph.d. i 1980, fik han en forskerstilling på Institute of Mathematics ved USSR Academy of Sciences i Novosibirsk. I 1990 blev han ansat som professor ved University of Wisconsin-Madison. Udover professorater på University of Chicago (1994-1995) og Yale University (1995-2002), er han i dag Rita L. Atkinson Chair i matematik ved University of California, San Diego.

Professor Zelmanov er medlem af the US National Academy of Science, the American Academy of Arts and Sciences, the Korean Academy of Sciences, the Royal Academy of Spain og the Academy of Sciences of Brazil.

Her er uddrag (oversat fra tysk) fra laudatio leveret af Walter Feit (Yale University) fra Fields Medal Award ceremonien ved den Internationale Kongres for Matematikere i Zürich, 1994:

"Efim Zelmanov received the Fields Medal for his brilliant solution to the long-time open Restricted Burnside Problem. It is a problem deep-rooted in group theory, the basis for the mathematical study of symmetries. What is asked for is a bound for the number of symmetries of an object, when each symmetry has bounded order.

Prior to the solution of the Restricted Burnside Problem, Zelmanov had already made important contributions to the theory of Lie algebras and to that of Jordan algebras; these theories have their origins in geometry, respectively in quantum mechanics. Some of his results that were achieved there were of crucial importance for his group theoretical work. In this way, the unity of mathematics is once again documented and it shows how much seemingly far apart areas are connected and influence each other."

Jonathan Alperin (University of Chicago) kalder Zelmanovs løsning af Restricted Burnside Problem "a tremendous breakthrough and a real triumph” og fortsætter:

"His proof is awesome and at a level completely ahead of any previous work in algebra. It is notable for its sheer power, but also for the volcano of new techniques he developed to bring it to completion. His single effort has completely changed and advanced the whole field of algebra and given us a whole new field on which to operate.”

Læs mere om Efim Zelmanov:

• Personal webpage (UCSD)