My research interests revolve around spacetime singularities, black holes, and gravitational lensing. Spacetime singularity theorems are regarded as statements about physics, but they are also purely mathematical: they help to classify geodesically (in)complete Lorentz manifolds. One of my goals is to arrive at a deeper geometric understanding of this classi.cation, as well as a deeper geometric understanding of the relation between a spacetime singularity and a black hole. Beyond this, I am interested in the phenomenon of magni.cation in gravitational lensing. I am delighted to join Kavli IPMU, because it encourages interdisciplinary pursuits such as these.