# Infinitesimal Hilbert 16th problem

Mon, 20/04/2015 - 14:00

Speaker:

Prof. S. Yakovenko, Weizmann Institute

Seminar:

Place:

2nd floor Colloquium Room, Building 216

Abstract:

I will describe the current state of affairs in both the original Hilbert 16th problem

(on limit cycles of polynomial planar vector fields) and its relaxed version on zeros of

Abelian integrals. It turns out that the latter belong to a natural class of Q-functions

described by integrable systems of linear differential equations with quasiunipotent monodromy,

defined over the field of rational numbers. Functions of this class admit explicit (albeit very

excessive) bounds for the number of their isolated zeros in a way similar to algebraic functions.

This result lies at the core of the solution of the infinitesimal Hilbert problem, achieved with

Gal Binyamini and Dmitry Novikov.

The talk is aimed at a broad audience.

- Last modified: 25/05/2015