What is the core collapse supernovae (CCSN) mechanism? What is the structure of neutron rich nuclei? These are very interesting open questions in nuclear physics and astrophysics but seemingly unrelated since a core-collapse supernova is a system that is many orders of magnitude larger than a nucleus. However, CCSNe depend on weakly interacting neutrinos. And interestingly we also note that in neutron rich nuclei the neutron distributions can be probed with weak interactions via parity violating scattering. I am interested in neutral current weak interactions in several different neutron rich many body systems. In this seminar, I will talk about neutrino-nuclear matter interactions in core-collapse supernovae and their influence on CCSN mechanism and supernovae neutrino signals. I will also talk about electron parity violating scattering experiments which provide a powerful tool to investigate the neutron distributions in nuclei.