The analysis of stellar oscillations, known as asteroseismology, has enabled detailed studies of the internal structures of stars, particularly subgiants and red giants. These stars with outer convective envelopes exhibit many oscillation modes simultaneously, whose frequencies depend on the star’s properties and structure of the stellar interior. Because many areas of astrophysics depend on accurate stellar modeling, asteroseismology provides a vital tool for improving our understanding of how astrophysical systems evolve over time. The research described in this dissertation utilizes data from NASA’s Kepler and TESS missions to model stars in detail using their oscillation properties, thereby probing their interiors. I show that detailed asteroseismic modeling of individual oscillation modes provides a powerful and sensitive probe of convective boundary mixing in low-mass stars. These constraints translate directly into improved stellar ages and internal structure determinations, which are critical for using stars as tracers of the formation and evolution of the Milky Way. In the latter chapters of this dissertation, I describe detailed asteroseismic modeling efforts targeted at metal-poor stars in the Milky Way’s stellar halo. The results of these modeling studies reveal that stellar parameters obtained using detailed asteroseismology with individual mode frequencies differ from results obtained using the widely-used global asteroseismic scaling relations. These findings have important consequences for the use of asteroseismology in galactic archaeology studies, especially as upcoming missions aim to greatly expand the sample of asteroseismic target stars used in studying our galaxy.
