Research Interests
My research focusses on the interaction between geometry and partial differential equations (PDEs). Mainly my current interests can be described by one of two banners: (1) applying view-points and methods from (differential/pseudo-Riemannian/something else) geometry to the study of hyperbolic PDEs; and (2) solving inherently geometric problems by looking at their associated PDEs. An example of the former is my work on shock formation for quasilinear wave equations. Examples of the latter include my work in general relativity, as well as my work studying time-like constant mean curvature submanifolds of Minkowski space.