Abstract:
    The statistical connection between galaxies and dark matter halos is pivotal in connecting cosmological observation to theory. The assumptions made in galaxy–halo connection models reflect our understanding of galaxy physics and impact cosmological analyses. In this talk, I will discuss statistical tools used to constrain the galaxy–halo connection, especially its beyond-halo mass component, the secondary galaxy bias. We find that count statistics complement the traditional two-point correlation function, and largely improve the constraints. I will present observational constraints on the galaxy–halo connection, obtained from SDSS DR7 with count statistics. We find strong evidence for secondary galaxy bias in some samples. I will also introduce a new computational method which allows fast forward modelling of count statistics, and new observational results from the DESI One Percent Survey based on this method. Finally, I will talk about the role of the cosmic web in the galaxy–halo connection, in the IllustrisTNG simulations.