The Galaxy-Halo Connection Across Mass and Time

Dark matter halos are the fundamental building blocks in the growth of
structure and they provide the framework for our modern understanding
of galaxy formation. I will discuss the current state of the art in
our understanding of the connection between galaxy properties and
their dark matter hosts over a range of masses and redshifts. In the
context of a given cosmological model, I will show how the galaxy-halo
relation can be tightly constrained at low redshift, and how it can be
used to infer the full star formation histories of galaxies. This
model for the co-evolution of galaxies and LCDM halos is in excellent
agreement with a wide range of data, including the evolution of the
stellar mass function, galaxy clustering statistics, and the
statistics of satellites around Milky Way mass hosts. I will discuss
applications to several issues in cosmology, including modeling of the
faintest dwarfs and modeling galaxies for the largest galaxy surveys.