Recent Progress in Numerical Modeling of Core-Collapse Supernovae and Binary Neutron Star Mergers

Core-collapse supernovae (CCSNe) and binary neutron star mergers (BNSMs) are among the most energetic phenomena in the universe, playing central roles in the formation of compact objects (such as neutron stars and black holes) and the production of heavy elements. Understanding these events requires detailed numerical modeling that captures the interplay between macrophysics (e.g., hydrodynamics and gravity) and microphysics (e.g., weak interactions, the equation of state, and nucleosynthesis). In this talk, I will present recent progress in theoretical studies of CCSNe and BNSMs, highlighting how numerical simulations have advanced our understanding of explosion mechanisms in CCSNe, BNSM dynamics, and their observable signatures. I will then discuss key open issues in the theory, focusing on neutrino quantum kinetics, which governs neutrino transport, matter interactions, and flavor conversions. In particular, I will present our recent studies, including large-scale global simulations of neutrino quantum kinetics associated with collective neutrino oscillations. Finally, I will outline future directions toward more realistic simulations and their connection to multi-messenger observations.