Courses I'm teaching can be found on Blackboard.
Also Salman Khan is a way better teacher than I'll ever be. Go learn from his videos. They're incredible.


Existence of CMC Cauchy surfaces from a spacetime curvature condition (with Greg Galloway)

CMC Cauchy surfaces play an important role in mathematical relativity. Sadly they don't always exist. BUT they do exist if gravity is attractive in all directions.

Weakly trapped surfaces in asymptotically de Sitter spacetimes (with Piotr Chruściel and Greg Galloway)

Invisibility of trapped surfaces in asymptotically flat spacetimes is a classical result (here classical is defined as any result obtained before I started doing research). We prove an analogous statement for asymptotically de Sitter spacetimes.

Milne-like Spacetimes and their Symmetries

I accidentally made a controversial physical discovery, and now I don't know what to do.

Maximizers in Lipschitz spacetimes are either timelike or null (with Melanie Graf)

In spacetimes with below Lipschitz regularity, maximizers between causally related points can contain parts that are timelike AND parts that are null. This is fascinating because it drastically differs from classical theory, but it's also annoying when developing low regularity causality theory. Fortunately maximizers in spacetimes with Lipschitz regularity must be either completely timelike or completely null.

Topology and singularities in cosmological spacetimes obeying the null energy condition (with Greg Galloway)

Most singularity theorems assume the strong energy condition. However evidence of dark energy (or a belief in inflationary theory) shows that the strong energy condition does not strictly hold. We obtain singularities without the strong energy condition, but in its place, we assume the existence of a Cauchy surface exapnding in all directions.

Timelike completeness as an obstruction to C 0-extensions (with Greg Galloway and Jan Sbierski)

Should timelike completeness imply C 0-inextendibility? Yes. Yes it should. Does it? We don't know. BUT timelike completess plus global hyperbolicity does imply C 0-inextendibility.

Some remarks on the C 0-inextendibility of spacetimes (with Greg Galloway)

We generalize some of Sbierski's methods from his pioneering paper on the C 0-inextendibility of the Schwarzschild spacetime. We obtain a structural result on spacetime boundaries and prove some inextendibility theorems within the class of spherically symmetric spacetimes.