Sub-millimeter observations with the revolutionary SCUBA (Sub-millimeter Common-User Bolometer Array) camera on the James Clerk Maxwell Telescope revealed the existence of a population of dust-obscured ultra-luminous galaxies at high redshifts that constitutes a substantial fraction of the cosmic far-infrared background. A full determination of many aspects of the history of the universe requires a comprehensive understanding of this dust-enshrouded galaxy population, and although enormous progress has been made, there are still many areas of uncertainty. One difficulty arises with galaxies with no known radio or X-ray counterpart, whose distance (redshift) cannot be measured because their location on the sky is only poorly known. The new Sub-millimeter Array telescope will be able to provide accurate positions and thus to fix this problem. In addition, the paucity of information about faint sources will be addressed with deep sub-millimeter observations in a region of the sky that has both current and planned data in various other wavelength regions. This research is fundamental to understanding the star formation and active galactic nucleus histories of the Universe, and will form the thesis of a graduate student, who will be well trained in this burgeoning field.