Stars are self-gravitating fluids in which many types of waves can propagate. Constructive interference of these waves produces global modes of oscillation, the associated brightness fluctuations of which can be detected and Fourier analysed to yield information about the stellar properties. Observations have revealed that a significant fraction of red giant stars have lower than expected amplitudes in their dipole modes, implying larger damping rates of these modes than for the rest of the population (the "dipole dichotomy" problem). Indirect evidence points towards the role of a deeply-buried magnetic field, but a detailed understanding of how gravity waves interact with strong fields is thus far lacking.

In this talk, I will present the results of recent work attacking the problem through a variety of linear, nonlinear, analytical and numerical approaches. We uncover a rich variety of physical processes that emerge when the field strength exceeds a certain critical threshold. In particular, we find that resonant interactions between gravity waves and Alfvén waves can lead to a singularity that produces efficient damping through viscous dissipation. Predicted damping rates are on par with those associated with convection, and lie in the range required to explain observations.