centra

Understanding the properties of matter inside neutron stars is a long standing problem. It is a challenge from both the theoretical and observational point of view, due to the complex physics involved in the structure of neutron stars: superfluidity, superconductivity, magnetic fields, solid and pasta phases, etc. Asteroseismology tries to constrain the properties of neutron star matter through the study of neutrons star oscillations, which may leave an observational imprint. In this talk, I present results in two different contexts. On the one hand, quasi-periodic oscillations have been observed during the X-ray tail of giant flares in magnetars. Those are thought to be internal magneto-elastic oscillations of the highly magnetised interior and the solid crust. I present results on the numerical modelling of this astrophysical scenario and how can it be used to put constraints on the properties of matter at high densities. On the other hand, gravitational wave signals from core collapse supernovae may be understood in terms of normal oscillations modes of proto-neutron stars excited during the post-bounce phase before the onset of the SN explosion. The observation of such modes in the future by gravitational wave observatories (Virgo, LIGO) may allow to infer properties of proto-neutron stars.