Neutrino flavor oscillations in the astrophysical and cosmological context often require to go beyond the usual amplitude-level treatment that is typical for laboratory applications. Instead, a Boltzmann kinetic equation in terms of matrices of densities in flavor space is required that captures in a consistent way both the effect of oscillations, the refractive effect of a background medium, and collisions. We propose to study Boltzmann kinetic equations for neutrino oscillations in various astrophysical and cosmological settings where a background medium or neutrinos themselves play a major role. We propose to develop this formalism further to allow for numerical solutions in terms of a Monte Carlo event-generator treatment that will be applied to neutrinos produced by dark matter annihilation in the Sun or Earth and to neutrinos emitted from the collapsed core of a supernova where both collisions and collective neutrino-neutrino refractive effects are important. In addition, it is proposed to study the Boltzmann kinetic equation that governs flavor effects in leptogenesis.
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