Multi-hadron interactions from lattice QCD

QCD is well-established as the correct theory for describing the strong nuclear force. However, the difficulty in using QCD at low energies makes connecting experiment to QCD challenging. Fortunately, lattice QCD offers a systematically improvable first-principles approach for studying QCD. This makes it a great tool for understanding e.g. the plethora of exotic-hadron candidates observed over the past couple decades, among other puzzling resonances like the Roper and $\Lambda(1405)$, and addressing how these states arise from QCD. In this talk, I will review the methods for constraining multi-hadron interactions from lattice QCD, with examples of systems that are straightforward to study. I will then focus on calculations for two nucleon interactions, which have a long history of disagreement from different collaborations, but are beginning to converge through the use of state-of-the-art methods for reliably extracting finite-volume spectra. Finally, I will describe efforts towards pushing the limits of the three-particle generalizations of the methods used in the two-particle cases, which are needed to study the many three-body resonances found in nature.