A major progress has been made in neutrino physics after the discovery of the neutrino oscillations. Crucial questions are being addressed experimentally and should receive an answer soon, including the absolute neutrino mass and mass ordering, the existence of sterile neutrinos and of CP violation in the lepton sector. Intriguing open issues also concern how neutrinos modify their flavor in astrophysical environments. In fact novel neutrino flavour conversion phenomena are currently being uncovered by theoretical investigations of neutrino propagation in core-collapse supernovae, accretion discs around compact systems, namely black holes and binary neutron star mergers.

            The thesis will focus on the theoretical investigation of the novel flavour conversion effects of neutrinos in media, in order to unravel the conditions for their occurrence, their nature and their impact either on the supernova explosion mechanim, or on the nucleosynthesis of  heavy elements in binary neutron star mergers, and/or on future observations of supernova neutrinos.

            We are at the verge of solving two longstanding open issues : i) how core-collapse supernovae explode, since three dimensional simulations are close to being succesfull ; ii) where are the heavy elements made, with the first observation of gravitational waves from binary neutron stars and a kilonova. The thesis aims at addressing the  role of neutrinos in this context, in connection with key neutrino properties and new flavor phenomena.