Theoretical developments in supernova neutrino physics : mass corrections and pairing correlators

We highlight the progress in our understanding of how neutrinos change their flavor in astrophysical environments, in particular effects from the neutrino self-interaction. We emphasize extended descriptions of neutrino propagation in massive stars that are beyond the current one based on the mean-field approximation. The extended equations include, in particular, corrections from (anti)neutrino-(anti)neutrino pairing correlations and from the neutrino mass. We underline open issues and challenges.