  We present a study of the evolution of the galaxy Velocity Dispersion
Function (VDF) from z=0 to z=1.5 using photometric data from the UKIDSS Ultra
Deep Survey (UDS) and Newfirm Medium Band Survey (NMBS) COSMOS surveys. The VDF
has been measured locally using direct kinematic measurements from the Sloan
Digital Sky Survey, but direct studies of the VDF at high redshift are
difficult as they require velocity dispersion measurements of many thousands of
galaxies. Taylor et al. (2010) demonstrated that dynamical and stellar mass are
linearly related when the structure of the galaxy is accounted for. We show
that the stellar mass, size and S\'ersic index can reliably predict the
velocity dispersions of SDSS galaxies. We apply this relation to galaxies at
high redshift and determine the evolution of the inferred VDF. We find that the
VDF at z~0.5 is very similar to the VDF at z=0. At higher redshifts, we find
that the number density of galaxies with dispersions <~200 km/s is lower, but
the number of high dispersion galaxies is constant or even higher. At fixed
cumulative number density, the velocity dispersions of galaxies with
logN[Mpc^{-3}]<-3.5 increase with time by a factor of ~1.4 from z~1.5-0,
whereas the dispersions of galaxies with lower number density are approximately
constant or decrease with time. The VDF appears to show less evolution than the
stellar mass function, particularly at the lowest number densities. We note
that these results are still somewhat uncertain and we suggest several avenues
for further calibrating the inferred velocity dispersions.
