Masterclass MINT 21/10/2026

mercredi 21 oct. 2026, 12:15 → 13:15 Europe/Paris

Salle F. Pellos (1R2-207) (Institut de Mathématiques de Toulouse (IMT))

Speaker : Benoît Bertrand

Title A glance at Hilbert 16th problem.

A real plane algebraic curve of degree d is the cancellation locus of a degree d real polynomial.
This set of real zeroes can have many connected components (but not too many, by Harnack's theorem). 
The first part of Hilbert 16th problem is about the possible relative positions of these components.
In general this is a wide-open problem. The solution is only completely know up to degree 7.
I will explain some properties of these curves, set up the problem, and explain methods that lead to the classification of the curves up homeomorphism of the ambient plane in very small degrees.