Testing the nature of dark matter and galaxy formation with small-scale structure

The abundance of low mass halos provides a fundamental constraint of the nature of dark matter via the free-streaming length. Models with GeV scale dark matter (Cold Dark Matter) match observations of galaxies remarkably well for galaxy masses above that of the Milky Way. At lower masses, such comparisons become more difficult as galaxies become fainter, and theoretical predictions for how galaxies form become more uncertain. I will present my work which involves two complementary approaches to measuring the abundance of small scale structure. First I discuss my measurements of the number of low mass galaxies across more than half the age of the Universe and in a variety of environments, and demonstrate how these measurements provide a deeper understanding of the physics of star formation in low mass dark matter halos. I will also present my novel approach to strong gravitational lensing which makes it possible to detect a much larger number of low mass dark matter halos even if they do not have any gas or stars. I will conclude by discussing future prospects for these programs given the next generation of ground and space based facilities.