Resolving ambiguities in the neutrino mass-flavour spectrum from supernova neutrinos

We analyze the neutrino conversions inside a supernova in the 3$\nu$ mixing scheme, and their effects on the neutrino spectra observed at the earth. We find that the observations of the energy spectra of neutrinos from a future galactic supernova may enable us to identify the solar neutrino solution, to determine the sign of $\mathrm{\Delta }{m}_{32}^2$, and to probe the mixing matrix element |U_{e3}|^2 to values as low as 10^{-4}-10^{-3}.