Studies in stellar oscillations and rotation with applications to compact objects

When stars die, they leave behind extremely dense remnants such as neutron stars and white dwarfs. These dead stars offer a wealth of information on, and provide observational tools to explore, questions related to cosmology, stellar evolution, and even the ripples in spacetime predicted from general relativity. Motivated by both electromagnetic and gravitational wave observations of compact objects, this thesis explores questions related to stellar evolution and interiors. In particular, we investigate waves excited by convective burning in stars, and study stellar rotation, just before supernova, and also waves excited through tidal interactions between pairs of white dwarfs.