A Guide to the Russian Academy of Sciences - University of Texas ...

Kudryavtsev, E. F. Mishchenko, S. M. Nikol'skii, I. G. Petrovskii, Iurii V.
Prokhorov, and A. G. Sergeev. The Vice-Directors at the Leningrad (Sankt
Petersburg) Branch have been A. A. Markov, N. P. Erugin, G. I. Petrashen, and
L. D. Faddeev.
(1996 update)
The Steklov Mathematics Institute: In 1996, the institute had some 16
departments and/or laboratories, as compared with 10 in 1989.
1. Department of Mathematical Logic: The Department of Mathematical Logic at the
Steklov Mathematical Institute was organized in 1957 at the recommendation of the
second All -Union Mathematical Congress which was held in Moscow in 1956.
The first Head of the Department was Petr Sergeevich Novikov. In 1973, by the
request of P. S. Novikov , S. I. Adian was appointed Head of Department. The
present staff of the Department, besides S. I Adian , are G. S. Makanin (since
1966), V. N. Grishin (since 1975), S. N. Artemov (since 1980), N. N. Repin
(since 1984), A. A. Razborov (since 1987), I. G. Lysionok (since 1990) and L. D.
Beklemishev (since 1991).
The traditional directions of research in the Department are connected with algorithmic
problems of algebra and with combinatorial group theory. The results obtained at
the Department always were among the most advanced results in the world in this
area. One can mention here P. S. Novikov's result on non-solvability of the identity
problem in Group theory (he received a Lenin prize for it in 1957); S. I. Adian's
theorems on non-recognizability of group properties (a Chebyshov prize in 1963); a
negative solution of the famous Burnside problem about periodic groups obtained
by P. S. Novikov and S. I. Adian . The method of classification of periodic words
introduced by them was improved and used for solution of a number of other wellknown
and difficult problems of group theory. One can also mention G. S.
Makanin's results on existence of algorithms for recognition of solvability of
arbitrary systems of equations in free groups and semigroups. Besides these
traditional topics in the Department in recent years, the theory of proofs (S. N.
Artemov, L. D. Beklemishev) and the theory of complexity of calculations (A. A.
Razborov) were developed. A. A. Razborov, for his lower estimates of the
complexity of calculations of Boolean functions, was awarded a Nevanlinna prize at
the International Congress of Mathematicians in Tokyo. Members of the
Department were invited speakers at the International Congress of Mathematicians
in Stockholm (1962, P. S. Novikov ), Nice (1970, S. I. Adian ), Helsinki (1978,
G. S. Makanin ), Berkeley (1986, A. A. Razborov).
2. Laboratory of Analytic Number Theory: The Department of Number Theory
was set up in 1934. I. M. Vinogradov was its Head from 1934 until 1983. At
different times, K. K. Mardzhanishvili, A. O. Gelfond, B. I. Segal, L. G.
Shnirelman, N. M. Korobov, A. G. Postnikov, L. P. Postnikova, N. V.
Kuznetsov, K. I. Oskolkov, S. A. Stepanov, A. I. Vinogradov worked in the
department.
The most brilliant research achievements in the Department include: a new method of
estimates of H. Weil's sums and its applications in number theory; an asymptotic
formula for the number of representations of an odd number by a sum of three
prime numbers; and, as a corollary of this formula, the solution of the Goldbach
problem; the theory of trigonometric sums with prime numbers; the solution of the
seventh Hilbert problem on transcendency of the logarithms of algebraic numbers;
rational approximations of linear forms of algebraic numbers and Diophantine
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