学术讲座
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:2018年3月13日 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.