  State-of-the-art numerical simulations of core-collapse supernovae reveal
that the main source of gravitational waves is the excitation of proto-neutron
star modes during post-bounce evolution. In this work we derive universal
relations that relate the frequencies of the most common oscillation modes
observed, i.e. g-modes, p-modes and the f-mode, with fundamental properties of
the system, such as the surface gravity of the proto-neutron star or the mean
density in the region enclosed by the shock. These relations are independent of
the equation of state, the neutrino treatment, and the progenitor mass and
hence can be used to build methods to infer proto-neutron star properties from
gravitational-wave observations alone. We outline how these measurements could
be done and the constraints that could be placed on the proto-neutron star
properties.
