  Let $z_1, \dots, z_m$ be $m$ distinct complex numbers, normalized to $|z_k| =
1$, and consider the polynomial $$ p_{m}(z) = \prod_{k=1}^{m}{(z-z_k)}.$$ We
define a sequence of polynomials in a greedy fashion, $$ p_{N+1}(z) = p_{N}(z)
\left(z - z^*\right)\qquad \mbox{where}~z^* = \arg\max_{|z|=1} |p_{N}(z)|,$$
and prove that, independently of the initial polynomial $p_m$, the roots of
$p_{N}$ equidistribute in angle at rate at most $(\log{N})^2/N$. This even
persists when sometimes adding `adversarial' points by hand. We rephrase the
main result in terms of a dynamical system involving the inverse fractional
Laplacian $(-\Delta)^{-1/2}$ and conjecture that, when phrased in this
language, the underlying regularity phenomenon might appear in a very general
setting.
