题目：Computable models --With introduction to Sobolev Institute of Mathematics in Russia
主讲：Prof. Sergey S. Goncharov，Member of Academy of Sciences in Russia
时间：上午10:00am - 11:00am
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.
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 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.