Tracing the formation history of galaxy clusters into the epoch of
  reionization
  The large-scale overdensities of galaxies at z~2-7 known as protoclusters are
believed to be the sites of cluster formation, and deep, wide survey projects
such as the Large Synoptic Survey Telescope (LSST) and the Wide Field Infrared
Survey Telescope (WFIRST) will deliver significant numbers of these interesting
structures. Spectroscopic confirmation and interpretation of these targets,
however, is still challenging, and will require wide-field multi-plexed
spectroscopy on >20 m-class telescopes in the optical and near-infrared. In the
coming decade, detailed studies of protoclusters will enable us, for the first
time, to systematically connect these cluster progenitors in the early universe
to their virialized counterparts at lower redshifts. This will allow us to
address observationally the formation of brightest cluster galaxies and other
cluster galaxy populations, the buildup of the intra-cluster light, the
chemical enrichment history of the intra-cluster medium, and the formation and
triggering of supermassive black holes in dense environments, all of which are
currently almost exclusively approached either through the fossil record in
clusters or through numerical simulations. Furthermore, at the highest
redshifts (z~5-10), these large extended overdensities of star-forming galaxies
are believed to have played an important role in the reionization of the
universe, which needs to be tested by upcoming experiments. Theory and recent
simulations also suggest important links between these overdensities and the
formation of supermassive black holes, but observational evidence is still
lacking. In this white paper we review our current understanding of this
important phase of galaxy cluster history that will be explored by the next
generation of large aperture ground-based telescopes GMT and TMT.
