Supernovae are among the most magnificent events in the observable universe. They produce many of the chemical elements necessary for life to exist and their remnants—neutron stars and black holes—are interesting astrophysical objects in their own right. However, despite millennia of observations and almost a century of astrophysical study, the explosion mechanism of supernovae is not yet well understood. Hyper-Kamiokande is a next-generation neutrino detector that will be able to observe the neutrino flux from the next galactic supernova in unprecedented detail. In this thesis, I investigate how well such an observation would allow us to reconstruct the explosion mechanism. I develop a high-precision supernova event generator and use a detailed detector simulation and event reconstruction to explore Hyper-Kamiokande’s response to five supernova models simulated by different groups around the world. I show that 300 neutrino events in Hyper-Kamiokande—corresponding to a supernova at a distance of at least 60 kpc—are sufficient to distinguish between these models with high accuracy. These findings indicate that, once the next galactic supernova happens, Hyper-Kamiokande will be able to determine details of the supernova explosion mechanism.