Van der Waerden/Schrijver-Valiant like Conjectures and Stable (aka Hyperbolic) Homogeneous Polynomials : One Theorem for all

Leonid Gurvits

Let $p$ be a homogeneous polynomial of degree $n$ in $n$ variables, $p(z_1,...,z_n)=p(Z)$, $Z\in C^n$. We call such a polynomial $p$ {\bf H-Stable} if $p(z_1,...,z_n)\ne 0$…