Faint dwarf galaxies, which are hosted in low dark matter halos, are key laboratories for probing cosmology and the nature of dark matter. There have been long standing debates in the literature on whether the observed properties of dwarf galaxies are consistent with the predictions of LCDM. I quickly discuss some of the key challenges and open questions in understanding dwarf galaxies in the cosmological context, in particular the galaxy-halo connection at the low mass end. I will show the results from two new cosmological simulations suites that my group has been working on. Using a large statistical sample of simulated dwarfs at intermediate resolution, I discuss the origin of scatter in the stellar mass-halo mass relation in the regime of classical dwarf galaxies (Mstar>10^5), and the associated observable signatures. I further show new results from Lyra cosmological simulations of ultra faint dwarf galaxies, with an unprecedented resolution of 4Msol, the highest resolution cosmological simulations ever attempted to z=0.
Andrii and Helena