2 problems

Infinitesimal Hilbert 16th conjecture. For any Darbouxian class $\mathscr D(m_1,\dots,m_n)$ and any degree $m_0$, there exists a finite number $N=N(m_0,m_1,\dots,m_n)$ such that an…

Uniform boundedness conjecture. For any pair of rational $1$-forms $(\theta,\omega)$ on the real plane $\mathbb R^2$ of degrees $n,m$ respectively, such that $d\theta=0$ and…