Neutrino flavor conversion in core-collapse supernovae and neutron star mergers

Neutrino flavor conversion is one of the major uncertainties in modeling dense astrophysical environments, such as core-collapse supernovae (CCSNe) and neutron star mergers (NSMs). In these extremely neutrino-dense systems, flavor conversion is nonlinear due to coherent neutrino-neutrino forward scattering, which can affect multiple aspects of the evolution, including the explosion dynamics, neutrino and gravitational-wave signals, heavy-element nucleosynthesis, and kilonova light curves. In this talk, I will review the main challenges in incorporating neutrino flavor conversion into simulations of CCSNe and NSMs, summarize the theoretical progress made so far, and outline a path forward for modeling neutrino oscillations in astrophysical sources.