Sergei Yakovenko
The Gershon Kekst Professor
The subject that intrigues me can
be described as analytic properties of objects (functions, curves etc.) defined
by polynomial ordinary differential equations. The most known paradigm in this
area is the Hilbert 16th problem, the last unsolved question from the known
Hilbert's list of 1900. This problem consists in determining the number of periodic
(closed) solutions of a polynomial differential equation with two variables.
In particular, together with Dmitry Novikov we succeeded in describing all functional fields which resemble the field of algebraic functions in the sense that the number of isolated zeros of each function from the field can be explicitly majorized. Quite surprisingly, this turns out to be in direct connection with one of the versions of the initial Hilbert problem. On the other side, an unexpected link to yet another Hilbert problem (21st), transpired.
Recent publications
- Bounded decomposition in the Brieskorn lattice and Pfaffian Picard-Fuchs systems for Abelian integrals. Bull. Sci. Math. 126 (7) (2002) 535-554.
- [with D. Novikov] Quasialgebraicity of Picard-Vessiot fields. Mosc. Math. J. 3 (2) (2003) 551-591,
- [with D. Novikov] Lectures on meromorphic flat connections. In: Normal forms, Bifurcations and Finiteness Problems in Differential Equations (Y. Ilyashenko and C. Rousseau, eds.), Kluwer, 2004.