  A nascent neutron star resulting from stellar collapse is a prodigious source
of neutrinos of all flavors. While the most basic features of this neutrino
emission can be estimated from simple considerations, the detailed simulation
of the neutrinos' decoupling from the hot neutron star is not yet
computationally tractable in its full glory, being a time-dependent
six-dimensional transport problem. Nevertheless, supernova neutrino fluxes are
of great interest in connection with the core-collapse supernova explosion
mechanism and supernova nucleosynthesis, and as a potential probe of the
supernova environment and of some of the neutrino mixing parameters that remain
unknown; hence a variety of approximate transport schemes have been used to
obtain results with reduced dimensionality. However, none of these approximate
schemes have addressed a recent challenge to the conventional wisdom that
neutrino flavor mixing cannot impact the explosion mechanism or r-process
nucleosynthesis.
