Weak Signal, Strong Background -- theoretical developments in the interaction of neutrinos with nuclei

A number of exciting large-scale international experimental efforts are underway which seek to use neutrinos to learn about extreme astrophysical environments or physics beyond the Standard Model. Such experiments necessarily involve neutrinos interacting with atomic nuclei, which presents a considerable challenge because hadronic and many-body effects constitute a complicated and non-negligible source of background. Effective field theory and ab initio many-body methods provide a promising path to a controlled treatment with quantified uncertainties. I will provide an overview of recent progress in theoretical treatment of neutrino-nucleus interactions, with particular emphasis on matrix elements relevant for neutrinoless double beta decay.