Information
Membership Number: FCA2305
Membership Type: Fellowship
Division: Mathematics and Information Sciences
Corresponding Email: *****nov@mi-ras.ru
Homepage(s): https://new.ras.ru/staff/akademiki/platonov-vladimir-petrovich/
Present and Previous Positions
Principal Researcher of "Federal Scientific Center Research Institute of System Studies of the Russian Academy of Sciences"
Fields of Scholarship and Research Interests
Mathematics: algebra, algebraic geometry, theory of numbers, topology
His interests are algebra, algebraic geometry and number theory. He solved the Strong approximation problem, developed the reduced K-theory and solved the Tannaka–Artin problem. He solved the Kneser–Tits and Grothendieck problems. Together with F. Grunewald he solved the arithmeticity problem for finite extensions of arithmetic groups and the rigidity problem for arithmetic subgroups of algebraic groups with radical. Platonov solved the rationality problem for spinor varieties and the Dieudonne problem on spinor norms. Platonov was an invited speaker of the International Congresses of Mathematicians in Vancouver (1974), Helsinki (1978) and the European Congress of Mathematicians in Budapest (1996).
Created a general method for the study of linear groups based on algebro-geometric and number-theoretic ideas.
Solved the problem of strong approximation in algebraic groups and the Kneser-Tits problem.
Developed the reduced K-theory and solved the Tannak-Artin problem on this basis.
Solved the rationality problem of spinor manifolds and the Dieudonné problem on spinor norms.
He investigated the local-global principle, according to which the structure of groups defined over arithmetic fields is determined by the structure of their localizations over the corresponding replenishments.
He proved the main approximation theorem for linear groups with a finite number of formers.
He constructed the theory of the most important classes of locally compact topological groups.
He discovered a new local-global principle for functional hyperelliptic fields defined over the field of algebraic numbers.
Together with his students, he solved the rationality problem for group algebraic manifolds over local and global fields.
Constructed the theory of finite-dimensional genzele bodies.
Solved Grothendieck's problem on finite replenishments of groups and the rigidity problem for arithmetic subgroups of algebraic groups with radical.
Developed the multiplicative theory of finite-dimensional bodies.
Solved the arithmeticity problem for polycyclic groups.
Developed a new approach to the congruence problem based on the analysis of combinatorial properties of arithmetic groups.
He constructed the fastest algorithms for computing S-unit groups in elliptic and hyperelliptic fields with a finite field of constants.
Honors, Awards and Other Membership
Full Member (Academician) of the Russian Academy of Sciences
Foreign Member of the Indian National Academy of Sciences
Honorary Member of Henan Academy of Sciences (China)
Member of the Creativity Academy (Science, Culture, Public Activity) (Moscow)
Academician of the Belarusian Academy of Education (BelAE)
Member of the New York Academy of Sciences
Member of the American Mathematical Society
Member of the Canadian Mathematical Society
1968: Lenin Komsomol Prize, for a series of works in topological group theory
1978: Lenin Prize in Science and Technology, for a fundamental series of works "Arithmetics of Algebraic Groups and Reduced K-Theory" ("Арифметика алгебраических групп и приведенная К-теория")
1993: Recipient of the Humboldt Prize (Germany)
Order of the Red Banner of Labour
Gold Medal, Russian Academy of Sciences
P.L. Chebyshev Gold Medal - for outstanding results in the field of mathematics, Russian Academy of Sciences
Selected Publications
https://csl.bas-net.by/personalii/80068/platonov-vladimir-petrovich/
Other Information
https://web.archive.org/web/20041020115310/http://www.ac.by/members/academicians/platonov.html