Universality conjecture for the microscopic roots of random polynomials

Let $f_n(z)=\sum_{j=0}^n\varepsilon_j z^j$, where $\{\varepsilon_j\}_j$ are iid real random variables satisfying $\mathbb{E}\,\varepsilon_1=0$ and $\mathbb{E}\,\varepsilon_1^2=1$. Universality conjecture. The conclusion of Theorem 1.1 still holds: the rescaled zero set $\{(|\zeta|-1)n^2:f_n(\zeta)=0\}$ converges, as $n\to\infty$, to a homogeneous Poisson process with intensity $1/12$, in the vague topology. This is proposed as a target for future research and is not proved in the paper.