  Neutrino flux streaming from a supernova can undergo rapid flavor conversions
almost immediately above the core. Focusing on this region, we study these fast
conversions using a linear stability analysis. We find that, for realistic
angular distributions of neutrinos, fast conversions can occur within a few
nanoseconds in regions just above the neutrinosphere. Our results also show
that neutrinos travelling towards the core make fast conversions more rapid.
These conversions, if they exist, can have significant implications for
supernova explosion mechanism and nucleosynthesis.
