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Neutrino flavor conversions are known to play a very important role in core-collapse supernova explosions. Inside a supernova, neutrino density is so large that neutrino-neutrino interactions take place, giving rise to "collective oscillations" occurring with a rate much larger than the usual MSW flavor conversions. In this talk, I would like to discuss some of the interesting aspects of these rapid flavor conversions, and the impact they can have on supernova explosions and nucleosynthesis. Finally, I will also talk about a simple way of diagnosing the presence of these instabilities in large scale numerical simulations.
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