The properties of the neutrino are imprinted on the evolutionary history of our Universe. In particular, the mass of the neutrino and its behavior has affected matter dominance, galactic structure, heavy element creation, and many other fundamental characteristics of the cosmos. Towards a complete understanding of the neutrino, the remaining mysteries mainly revolve around answering a singular question: How often do muon neutrinos turn into electron neutrinos? The multi-faceted answer is one of the keys to bringing us into the age of astroparticle physics, in which we relate the smallest (particle) and largest (cosmic) scales.

In this talk, I will present our work in studying muon-to-electron neutrino mixing at both short and long distances, utilizing powerful accelerators and ultra-large detectors in the US and Japan.