Justin Read - January 23, 2015 The edge of galaxy formation The LCDM cosmological model has been tremendously successful at explaining a host of observational data on scales larger than ~1Mpc. However, on smaller scales there have been two long standing puzzles: the cusp/core and missing satellites problems. While many solutions have been suggested for both, it remains unclear whether the full solution lies purely in "baryonic physics" or whether we must modify the cosmological model on small scales. In this talk, I show how we can make progress by focussing on the very smallest galaxies in the Universe. I present two new methods for weighing these tiny galaxies, the former making use of tidal distortions at their edges; the latter using ~4pc resolution simulations of isolated dwarfs (at which resolution, the simulations become insensitive to details of the 'sub-grid' modelling). Armed with a measure of the total mass, I show that either abundance matching below ~10^10 Msun fails or we must indeed consider modifications to LCDM. The striking implication of the former is that the Milky Way must be surrounded by many "dark dwarfs" that are more massive than their visible counterparts.