Parameter estimation of core-collapse supernovae (CCSN) is challenged by the unmodeled nature of post-bounce gravitational waveforms and by the intrinsic difficulties involved in the modeling of explosions of massive stars. Asteroseismology of proto-neutron stars (PNS) may offer a promising approach to do so. Numerical simulations of CCSN show that g-modes are commonly excited in PNS and they are responsible for a significant fraction of the gravitational-wave signal produced by most (i.e. neutrino-driven) supernova explosions. The time-frequency evolution of those modes is linked to the physical properties of the PNS through quasi-universal relations. This talk discusses recent work aimed at inferring PNS properties through the analysis of its modes of oscillation and the gravitational waves they provoke. Observational constraints of our findings for current and third-generation gravitational-wave detectors are also reported. If time permits the talk will also cover recent results for the rather specific case of rapidly-rotating CCSN.
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