Abstract
Neutrinos are weakly interacting particles. Due to their extremely small cross sections, neutrino absorption and scattering can be neglected in many astrophysical scenarios. However, at extremely high densities ($\rho \gtrsim 10^{13} \, {\rm g/cm^3}$) and temperatures ($T \gtrsim 10 \, {\rm GK}$), neutrinos represent a key ingredient to model correctly the dynamics of core collapse supernovae and neutron star mergers. In addition, they are crucial to determin the properties of the matter possibly ejected from these systems. This matter is expected to give a relevant contribution to the production of heavy elements in the Universe. Both the neutrino and the matter properties in such extreme conditions are sensitive to the nuclear EOS properties and, due to the expected neutron richness, to the nuclear symmetry energy. In this talk, I will present recent results concerning the role of neutrinos in stellar collapse and in the aftermath of neutron star merger, and briefly discuss possible dependences on the nuclear EOS. In the former scenario, effective models of spherically symmetric explosions with neutrino transport are presently the best available tool to explore systematically broad progenitor samples. In the latter, neutrinos are thought, in general, to influence the neutron richness of all the ejecta and, more specifically, to drive neutrino-driven outflows from the disc that results from the binary merger.