Abstract:I will present novel statistical methods to unveil the physical link between the observed galaxy properties and their underlying dark matter halos, using the measurements of spatial clustering, weak gravitational lensing, and marked statistics from the Sloan Digital Sky Survey (SDSS). In particular, I will describe the "iHOD" model, a powerful improvement to the Halo Occupation Distribution (HOD) formalism, which extracts maximum information on the galaxy-halo connection from galaxy surveys. The derived stellar-to-halo mass relation not only explains the clustering and lensing of SDSS galaxies, but also automatically reproduces the stellar mass functions observed in SDSS. By examining the weak lensing signals around red vs. blue galaxies, I will further demonstrate that the quenching of star formation activities in galaxies is primarily tied to the dark matter mass of halos, rather than the stellar mass or halo age assumed in several popular galaxy formation models (e.g., age-matching). I will also show that, the combination of this halo mass quenching and the environmental dependence of halo mass function can naturally explain the curious effect of large-scale galactic conformity, i.e., the observed correlation of galaxy colors over scales well beyond the 2-halo regime.