Dmitri Andreevich Gudkov

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Dmitri Andreevich Gudkow , Russian Дмитрий Андреевич Гудков , English transcription Dmitry Andreevich Gudkov, (born May 18, 1918 in Vologda ; † 1992 ) was a Russian mathematician. He succeeded in solving a significant part of Hilbert's 16th problem in real algebraic geometry.

Gudkov was the son of a surveyor (who died around 1919) and a doctor. In 1926 his mother moved with him to Nizhny Novgorod and in 1935 to Gorki, where Gudkov studied at the State University from 1936, graduating in 1941. After that, he was a soldier and also participated in the conquest of Berlin. From 1946 he was assistant at the University of Nizhny Novgorod and from 1954 lecturer at the chair of analysis. In 1961 he became a mathematics professor in the radiophysics department with a full professorship from 1971. In 1978 he was given the chair for geometry and higher algebra.

Gudkov received his doctorate in 1953 under Alexander Alexandrowitsch Andronow at the Lobachevsky University in Nizhny Novgorod . Andronow suggested studying the theory of bifurcations (his specialty) of solutions to differential equations using algebraic curves as an example. David Hilbert and Axel Harnack tackled the problem of the topological classification of planar algebraic curves via the deformation (small perturbations) of selected initial configurations. In his dissertation he said at the time that he had proven Hilbert's conjecture about the number of different topological configurations in the 16th Hilbert problem, but when he wanted to work this out for his habilitation in 1969 he found an error and another configuration besides the two by Harnack and Hilbert and completed the proof of this part of Hilbert's 16th problem (topological classification of the non-singular plane projective algebraic curves of degree 6). At the same time he made a conjecture about the topology of algebraic curves in the projective plane, which was partially proven in 1972 by Vladimir Arnold . In his attempt to prove the rest, Wladimir Abramowitsch Rochlin soon found that the conjecture was wrong and proved an expanded and corrected conjecture.

In 1992 his Russian biography of Nikolai Ivanovich Lobachevsky was published . He published some documents in it for the first time and clarified some questions of genealogy (for example that the alleged sons of Lobachevsky were not his, but those of surveyor Sergei Stepanowitsch Schebarschin (1748 / 49–1797)).

His hobbies were chess, fishing, gardening and mushroom picking.

Fonts (selection)

  • The topology of real projective algebraic varieties, Russian Mathematical Surveys, Volume 29, 1974, pp. 1-79
  • with AD Krakhnov: Periodicity of the Euler characteristic of real algebraic (M-1) manifolds, Functional Analysis and Its Applications, Volume 7, 1973, pp. 98-102
  • Ovals of sixth order curves, in: Nine Papers on Hilbert's 16th Problem, American Mathematical Society Translations 112, 1978, pp. 9-14
  • On the topology of algebraic curves on a hyperboloid, Russian Mathematical Surveys, Volume 34, 1979, No. 6, pp. 27-35

Web links

personal data
SURNAME Gudkow, Dmitri Andreevich
ALTERNATIVE NAMES Гудков, Дмитрий Андреевич (Russian); Gudkov, Dmitry Andreevich
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH May 18, 1918
PLACE OF BIRTH Vologda
DATE OF DEATH 1992