  Swarmalators are oscillators that swarm through space as they synchronize in
time. Introduced a few years ago to model many systems which mix synchrony with
self-assembly, they remain poorly understood theoretically. Here we obtain the
first analytic results on swarmalators moving in two-dimensional (2D) plane by
enforcing periodic boundary conditions; this simpler topology allows
expressions for order parameters, stabilities, and bifurcations to be derived
exactly. We suggest some future directions for swarmalator research and point
out some connections to the Kuramoto model and the Vicsek model from active
matter; these are intended as a call-to-arms for the sync community and other
researchers looking for new problems and puzzles to work on.
