  We present a new technique for observationally identifying galaxy mergers
spectroscopically rather than through host galaxy imaging. Our technique
exploits the dynamics of supermassive black holes (SMBHs) powering active
galactic nuclei (AGNs) in merger-remnant galaxies. Because structure in the
universe is built up through galaxy mergers and nearly all galaxies host a
central SMBH, some galaxies should possess two SMBHs near their centers as the
result of a recent merger. These SMBHs spiral to the center of the resultant
merger-remnant galaxy, and one or both of the SMBHs may power AGNs. Using the
DEEP2 Galaxy Redshift Survey, we have examined 1881 red galaxies, of which 91
exhibit [O III] and Hbeta emission lines indicative of Seyfert 2 activity. Of
these, 32 AGNs have [O III] emission-line redshifts significantly different
from the redshifts of the host galaxies' stars, corresponding to velocity
offsets of ~50 km/s to ~300 km/s. Two of these AGNs exhibit double-peaked [O
III] emission lines, while the remaining 30 AGNs each exhibit a single set of
velocity-offset [O III] emission lines. After exploring a variety of physical
models for these velocity offsets, we argue that the most likely explanation is
inspiralling SMBHs in merger-remnant galaxies. Based on this interpretation, we
find that roughly half of the red galaxies hosting AGNs are also merger
remnants, which implies that mergers may trigger AGN activity in red galaxies.
The AGN velocity offsets we find imply a merger fraction of ~30% and a merger
rate of ~3 mergers/Gyr for red galaxies at redshifts 0.34 < z < 0.82.
