Supernova neutrino oscillations: what do we understand?

We summarize our current understanding of the neutrino flavor conversions inside a core collapse supernova, clarifying the important role played by the "collective effects" in determining flavor conversion probabilities. The potentially observable $ν_e$ and $\barν_e$ spectra may help us identify the neutrino mixing scenario, distinguish between primary flux models, and learn more about the supernova explosion.

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