  We provide a lattice demonstration of $(2+1)$-dimensional field theory
dualities relating free Dirac or Majorana fermions to strongly-interacting
bosonic Chern-Simons-matter theories. Specifically, we prove the recent
conjecture that $U(N)$ level-1 with $N_f$ gauged complex Wilson-Fisher scalars
(where $1\le N_f\le N$) is dual to $N_f$ Dirac fermions, as well as the
analogous conjecture relating $SO(N)$ theories with real Wilson-Fisher scalars
to Majorana fermions for $1\le N_f\le N-2$. Furthermore, we discover new
dualities that allow us to explain the interesting phase structure of the
$SO(N)$ theories with $N-1$ and $N$ scalars, for all $N\ge 2$.
