Research

My work currently centres on the study of geometric data for regions in spacetime in order to find a representation for the physical mass contained within. A quick introduction and overview of my work can be found here. My most recent projects can be found here.

Relativity is a theory involving spacetime (three dimensions of space and one of time). Each of the three slices above represent all of space at three different instants of time. Associated with the top (tilted) slice is an observer traveling with respect to the black hole. The horizontal slices represent two freeze frames of space for another observer seeing a fixed black hole. Beautiful results by Bray and Huisken-Ilmanen in the late 90's answered a conjecture of Penrose linking the geometry of ``non-moving'' (our horizontal) slices with black holes and mass.

Another three-dimensional geometry of interest is the light cone off of a black hole horizon. Called a null cone, this conical slice (also shown above) is a collection of all the light rays hitting the surface of the black hole (two dimensions to pick a point on its surface and an additional dimension along the light ray through it). Null cones gives rise to a new approach for understanding the Penrose conjecture.