Probing dark matter and galaxy evolution with proper motions of galaxies
  We discuss several problems that can be solved by measuring the proper
motions of galaxies in clusters of galaxies, something that should be feasible
in the Next Generation Very Large Array era. First, in the Virgo Cluster, the
Laser Interferometric Space-based Antenna should provide standard siren
distances for a substantial number of galaxies which contain black hole-black
hole binaries. Measuring the proper motions of these galaxies will give
6-dimensional phase space information about the orbits of these galaxies,
providing a unique set of tracers of cluster dynamics. Additionally, in other
clusters proper motion measurements should allow the determination of whether
spiral galaxies are on their first infall into the cluster, and measurements of
the proper motions of galaxies in merging clusters will allow direct measures
of the speed of the merger, which can then be compared with estimates from
shocks.
