Gravitational Wave Lensing in the Presence of Substructure

Gravitational lensing is an invaluable probe of the nature of dark matter and the structures it forms. Lensed gravitational waves in particular allow for unparalleled sensitivity to small-scale structures within lenses, due to the precise time resolution combined with continuous monitoring of the entire sky. In this talk, I will explore the effects that the presence of dark matter substructures has on lensed gravitational waves, and show how we can both infer the presence of substructure through observed lensed signals, and constrain the nature of dark matter through their detection. If time permits, I will also highlight exciting prospects for gravitational-wave lensing in the strong field.