math.AP

This is an arXiv category tag for the analysis of partial differential equations.

Lecture slides that Gustav Holzegel and I used for the January 13-14, 2014 OXPDE Workshop at Oxford University.
Last updated on 2 min read expository

Lecture notes introducing Sobolev spaces.
Last updated on 1 min read expository

We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.
Last updated on 13 min read expository

Let us consider first the linear wave equation \[ \Box u = 0\] on (1+d)-dimensional Minkowski space. A well known property of the wave …
Last updated on 6 min read expository

Paper announcement and exposition.
Last updated on 6 min read research

My PhD Thesis on characterization and conditional uniqueness of the Kerr-Newman solution in general relativity.
Last updated on 2 min read research