The phase transition from a neutral to ionized Universe during the time of the first galaxies lies at the frontier of astrophysics. Determining the topology of the ionized regions during this epoch of reionization will provide powerful constraints on the properties of the first galaxies that have yet to be seen directly. Two observational pathways to probing the properties of these ionized bubbles exist: low-frequency radio observations of the redshifted 21 cm line of neutral hydrogen and the observations of the clustering of Lyman alpha emitter galaxies. Observations in each of these areas are expected to expand greatly over the next five years. This work will seek to understand the topology of ionized bubbles during reionization and so identify the key signatures of the first galaxies and reionization in 21 cm tomography. We will also explore new ways of using clustering of Lyman alpha emitting galaxies to probe reionization via the non-Gaussianity of the clustering and the cross-correlation between LAE and continuum galaxies. By including details of the underlying physical processes and observational techniques we will develop optimal statistics that are robust and realistic. This theoretical work will support the efforts of the many European observational programs, such as LOFAR and VISTA, seeking to determine the nature of reionization and the first galaxies.
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