  We provide a new analysis of the Boltzmann equation with constant collision
kernel in two space dimensions. The scaling-critical Lebesgue space is
$L^2_{x,v}$; we prove global well-posedness and a version of scattering,
assuming that the data $f_0$ is sufficiently smooth and localized, and the
$L^2_{x,v}$ norm of $f_0$ is sufficiently small. The proof relies upon a new
scaling-critical bilinear spacetime estimate for the collision "gain" term in
Boltzmann's equation, combined with a novel application of the Kaniel-Shinbrot
iteration.
