The Illustris project is a set of large-scale (approx. 10^6Mpc^3 in volume) cosmological simulations published in 2014, where the expansion of the universe, the gravitational pull of matter onto itself, the hydrodynamics of cosmic gas, as well as the formation of stars and black holes and their effects on their environments, are all modeled starting from initial conditions resembling the very young Universe 300,000 years after the Big Bang. We use the Arepo code, which offers significant advantages in modeling hydrodynamics to simulate the aforementioned processes. We have performed detailed comparisons of our simulation box to observed galaxy populations, and studied numerous aspects of the galaxy formation process as it appears in these simulations. An updated list of publications by our collaboration can be found here.
In the publications that I have led using Illustris, I focused on a review of the high-redshift galaxy population, on the origin of the angular momentum of low-redshift galaxies, and on the effects of galaxy environment on metallicity.
Our collaboration recently created the next generation of Illustris simulations, the IllustrisTNG project. In these, new physics models generate galaxy populations whose properties are even closer to reality, and galaxy populations are followed within a larger cosmological volume, or at significantly higher resolution. These simulations are hence even more powerful in allowing us to study how galaxies evolve over time. In my own studies of these simulations, I focused on the size evolution of galaxies over cosmic time.