have mass and can oscillate between flavors. The oscillations occur in vacuum, but can also be mediated by neutrino-electron scattering (the Mikheyev-Smirnov-Wolfenstein \[MSW\] effect) and neutrino-neutrino scattering. Neutrino oscillations depend on neutrino mixing parameters and on the neutrino mass eigenstates (the magnitudes of the mass differences are known, but not their signs). Observation of neutrinos from the next galactic core-collapse supernova could help constrain the neutrino mass hierarchy (see the recent review by [@mirizzi:16]).

    MSW oscillations occur in the stellar envelope. They are important for the neutrino signal observed in detectors on Earth, but they cannot influence the explosion itself. The self-induced (via neutrino-neutrino scattering) oscillations, however, occur at the extreme neutrino densities near the core. They offer a rich phenomenology that includes collective oscillation behavior of neutrinos (see the review in [@mirizzi:16]). The jury is still out on their potential influence on the explosion mechanism.

    Collective neutrino oscillation calculations (essentially solving coupled Schrödinger-like equations) are computationally intensive [@mirizzi:16]. They are currently performed independently of core-collapse supernova simulations and do not take into account feedback on the stellar plasma. Fully understanding collective oscillations and their impact on the supernova mechanism will quite likely require that neutrino oscillations, transport, and neutrino-matter 