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科研成果201804期 Computable models --With introduction to Sobolev Institute of Mathematics in Russia

16

2018-10

201804期 Computable m

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Computable models --With introduction to Sobolev Institute of Mathematics in Russia


主讲嘉宾: Professor Sergey S. Goncharov

(Member of Academy of Sciences in Russia)

时间:2018313 下午2:30

地址:深圳大学计算机与软件学院1楼报告厅



Biography of Sergey Goncharov

Professor Sergey Goncharov graduated with honours from the Department of Mechanics and Mathematics of Novosibirsk State University (NSU) in 1973 and defended thesis for candidatskaya degree in 1974. In 1976, he won Lenin Komsomol Prize on science and technology for a series of works on constructive Boolean Algebras. He became an associated professor at NSU. He defended thesis for doctorskaya degree in 1981 and was awarded with a Silver badge of Algebra and Logic Seminar for research activityin 1982. In 1983, he won Siberian Branch of Russian Academy of Sciences Prize for establishing the theory of semantic programming in cooperation with Yu. L. Ershov and D. I. Sviridenko. He became a professor at Novosibirsk State University in 1985 and an elector at Russian Academy of Sciences in 1991. He was elected to be a corresponding member of the Academy of Sciences of Higher School in 1993 and was elected to be a full member of the International Academy of Sciences of Higher School in 1995. In 1997, he was elected to be a corresponding member of the Russian Academy of Sciences. He won Mal'sev prize of Russian Academy of Sciences in 1997. In 2002, he was elected to be a member of the Russian Academy of Sciences. In 2013, he  was elected to be a member of the Presidium of Siberian Branch of Russian Academy of Sciences. In 2016, he was elected to be academician (full member) of the European Academy of Sciences. He won Lavrent’ev prize of Siberian Branch of Russian Academy of Sciences in 2017.

Abstract

Fields of research interest: theory of algorithms, model theory, algebra, and applications in theoretical computer science. Basing on the result on the existence of non-autostable models with finite algorithmic dimension, the theory of algorithmic dimension is developed. New methods to prove infinite algorithmic dimension are found. These methods made possible a solution to the problem of characterization of spectra of algorithmic dimension for series of concrete classes of models. A criterion of decidability for homogeneous models is established. Basing on it, solutions to problems of M. Morley and of Peretyatkin–Denisov were obtained. A solution to the Malcev problem on the characterization of classes of axioms with strong epimorphisms and strong homomorphisms is given. A series of results on constructive Boolean algebras is obtained. Nilpotent groups of finite algorithmic dimension were studied. A characterization is obtained for autostability of nilpotent torsion-free groups of finite rank as well as for Abelian pp-groups. A new method to construct computable numbering is suggested that made possible solutions to a series of problems on Friedberg numberings, on families with unique positive numbering, etc. A solution to the problem of autostability of finitary constant expansions was obtained together with American scientists R. Shore, B. Khoussainov, and P. Cholak. A solution to the problem of two-element spectrum with recursive TT-degree was obtained together with B.Khoussainov. A problem on a family with trivial Rogers semilattice but nontrivial inclusion was solved together with S. A. Badaev. A problem on the existence of strong constructive homogeneous extensions is solved. Together with an Italian logician A. Sorbi, the Rogers semilattice of computable numberings of arithmetical sets was investigated. Together with J. Knight (USA), the structure theory of computable classes of models is suggested, a problem of characterization of Σ11Σ11-relations on computable models is solved. More than 160 papers were published; among them are two manuals: "Lectures in model theory" and "Introduction to the logic and methodology of science" (with Yu. L. Ershov and K. F. Samokhvalov), monographs: "Countable Boolean algebras" (1988) and "Countable Boolean algebras and decidability" (1996, English translation 1997), "Constructive models" (1999, with Yu. L. Ershov, English translation 2000) and "Handbook of recursive mathematics" (1999, S. S. Goncharov, Yu. L. Ershov, A. Nerode, J. Remmel, V. Marek editors).

Sobolev Institute of Mathematics

Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences is located in Novosibirsk, Akademgorodok. The Institute was foundered in 1957 by Academician Sergey Sobolev. At present the Institute is directed by Member of RAS, Professor, Doctor of Sciences (Physics and Mathematics) Sergey Goncharov. The members of the Institute carry on fundamental investigations in mathematics, mathematical physics, and informatics in the following main directions:

  •  algebra, theory of numbers and mathematical logic;
  •  geometry and topology;
  •  calculas, differential equations and mathematical physics;
  •  probability and mathematical statistics;
  •  numerical mathematics;
  •  mathematical modeling and methods of applied mathematics;
  •  theoretical nuclear physics.

The investigations carried on at the Institute are supported by various domestic and interactive funds. In 2004, the Institute had 54 grants of  the Russia Foundation for Basic Research, 8 grants of the Russia Humanitarian Scientific Foundation, 4 grants of the Federal Pilot Program “Integration”, etc. In the frames of the state program for support of leading scientific schools, the grants were allotted to 7 scientific schools headed by A. A. Borovkov, Yu. L. Ershov, M. M. Lavrent’ev, Yu. G. Reshetnyak, S. S. Goncharov, V. L. Beresnev and V. A. Vasil’ev. State scholarships for prominent scientists are awarded to 20 members of the Institute, and 9 men received state scholarships for young scientists.

The Institute participates actively in training of highly qualified scientific personnel in cooperation with the Department of Mechanics and Mathematics of Novosibirsk State University.

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