The investigators will develop a formalism and physical models to describe the substructure and shapes of dark matter halos. Analytic models have assumed that the mass in the universe is bound up in halos which are both spherical and smooth, but numerical simulations now have sufficient resolution to show that they are actually triaxial and rather lumpy. This work will use gravitational lensing observations to constrain the small scale end of the cosmological mass power spectrum, to constrain halo profiles, and to interpret measurements of the cosmic shear field. It will support modeling the luminosity function of galaxies and its evolution, predicting the distribution of galaxies and gas in clusters, and the use of higher order statistics to break the degeneracy between cosmological parameters associated with measurements of two point statistics. The wide range of applications makes this work a good unified framework within which to introduce graduate and undergraduate students to topics in large-scale structure. ***
