Towards ab initio calculations of nuclear structure and matrix elements

Chiral effective field theory (EFT) describes the interactions relevant for the low-energy structure of nuclei, which in the recent years have become the standard for calculations of medium-mass nuclei. Theoretical calculations have been very successful in the description, and prediction, of experimental data. I will discuss some of these results, and present efforts that focus on estimating the theoretical uncertainties, especially those related to the nuclear hamiltonian. In addition, chiral EFT predicts the consistent electroweak currents that enter the transition operators that test fundamental symmetries. I will discuss double-beta decay matrix elements that combine phenomenological nuclear structure calculations and chiral EFT currents, as well as strategies to constrain the values of these matrix elements. Finally I will show results for the scattering of weakly interacting massive particles (WIMPs) off nuclei, which can also be formulated in terms of chiral EFT currents. I will cover results for the elastic and inelastic scattering cases, which can be used to determine the spin-dependent character of the WIMP-nucleus interaction.