Neutrino-nucleus reaction processes play important roles in the synthesis of 7 Li, 11 B, 138 La, 180 Ta and other elements in explosive environments realized in supernovae. We have constructed new shell-model Hamiltonians based on recent progress in the physics of exotic nuclei. The shell evolutions toward driplines and the spin responses of nuclei are found to be remarkably improved by the new Hamiltonians. Proper tensor components in the Hamiltonians are shown to be important for the improvements. We then applied these Hamiltonians to calculate the neutrino-nucleus reaction cross sections, and obtained more precise theoretical estimates of supernova nucleosynthesis of 7 Li, 11 B and 55 Mn etc, including the neutrino processes. Finally, we propose a new method for determining the neutrino oscillation parameter, the mixing angle θ 13 , and the mass hierarchy, by making use of the strong dependence of the yields of 7 Li and 11 B on these parameters.