| Abstract: Massive neutrinos suppress the growth of cosmic structure on small, non-linear, scales. There is thus much interest in using statistics beyond the power spectrum to tighten constraints on the neutrino mass by extracting additional information from these non-linear scales. In this talk, I will first explore the information in the non-linear matter field, showing that the power spectrum, halo mass function, and void size function can be combined to break degeneracies between cosmological parameters and give considerably tighter constraints on the neutrino mass compared to the power spectrum alone. I will then explore how much of this non-linear information we can expect to find in upcoming surveys which observe galaxy clustering, weak lensing, and the CMB. In turn, I will motivate field-level inference with differentiable forward modeling as a method to optimally extract information from cosmic structure and to reconstruct the initial conditions of the Universe. In particular, I will tackle one of the bottlenecks of this approach -- sampling a high-dimensional parameter space -- by presenting a novel sampling method, Microcanonical Langevin Monte Carlo. This method is orders of magnitude more efficient than the traditional Hamiltonian Monte Carlo and will enable scaling field-level inference to the regime of upcoming surveys. Finally, I will introduce the HalfDome cosmological simulations -- a set of large-volume simulations designed to model the Universe from CMB to LSS for the joint analysis of Stage IV surveys. I'll discuss how these simulations can be used to mitigate systematics, obtain tighter constraints on cosmological parameters, and as a playground for machine learning applications. Link to the Event Video |