The Nature of Dark Matter: 
There is robust observational evidence that approximately 85% of the mass in the universe is in the form of non-baryonic material, different from anything known in the periodic table of elements. The leading idea is that dark matter consists of elementary particles beyond the standard model of particle physics. Understanding the nature of dark matter and characterizing the microphysics of the dark matter particles stand among the most important quests in modern cosmology and particle physics. Much of my work focuses on the use of numerical simulations in comparison with astronomical observations to constrain the nature of dark matter, specifically on the “small” size-scales of individual galaxies. Interestingly, there are some indications that the standard cold dark matter model may not be able to reproduce some observations on small scales, which motivates the exploration of alternative models like self-interacting dark matter. The image above shows a simulation by former PhD student Shea Garrison-Kimmel of how dark matter may be distributed in the Local Group.
Here is a review article on the small scale crisis in cold dark matter I wrote with Mike Boylan-Kolchin.
Here is the original Too Big to Fail paper, where we pointed out one of the potential problems with cold dark matter.
Here is a self-interacting dark matter paper led by former PhD student Miguel Rocha, which used simulations to show how SIDM may help with small-scale problems.
Satellite Galaxies and Stellar Halos: The smallest galaxies in the universe are laboratories for galaxy formation in the extreme. Dwarf galaxies are the most dark-matter dominated, lowest metallicity, and most numerous galaxies in the universe and therefore provide important testing grounds for theories of galaxy formation and the nature of dark matter. One of my longstanding research themes has been to understand the character and overall count of small dwarf galaxies in the vicinity of the Milky Way. Many of the small galaxies that got close to the Milky Way in the past were completely destroyed by tidal interactions and their remnants are seen to exist as stellar streams and diffuse light in the stellar halo. Galaxy stellar halos therefore provide complementary laboratories for constraining galaxy formation physics and the merger histories of galaxies. The image here shows stars in the same simulation as above, now demonstrating how tiny satellite galaxies and diffuse stellar halo light may be distributed throughout the Local Group.
Here is a paper on stellar halo formation that I wrote with Kathryn Johnston.
Here is a paper led by former PhD student Joe Wolf that derived a new standard mass estimator for dwarf galaxies.
Here is a paper led by former PhD student Erik Tollerud that predicts the existence of many more dwarf galaxies soon to be discovered.
Galaxy Formation: Within the standard paradigm, the locations of galaxies in space and their global potentials are governed by dark matter halos. But the detailed properties of galaxies — their sizes, shapes, evolutionary histories, and chemical makeup — are driven by complex astrophysical properties. In order to fully understand galaxy formation, we must not only account for dark matter and dark energy, but also the baryonic material and associated astrophysics that governs stellar evolution, feedback, and the multiphase structure of cosmic gas. This image shows gas in the same simulation and illustrates how an extended Circum-Galactic Medium (CGM) of multiphase gas likely exists throughout the Local Group.
Here is a paper led by former PhD student Kyle Steward that introduced the idea that the gas that builds galaxies should have much more angular momentum than the dark matter.
Here are two papers led by former Postdoc Jose Oñorbe and former PhD student Coral Wheeler that simulate the formation of tiny galaxies using FIRE simulations.