Notes and slides

Some notes on geometric notion of derivatives PDF
Some very rough and unpolished notes summarizing some things that are quite well-known to the experts. May be helpful to those just gaining proficiency in differential geometry. This may be updated to be something more serious later.

Stability of de Sitter space under the Lorentzian constant mean curvature flow Prezi
On November 3, 2014, I will gave the GAPDE seminar at DPMMS. For this talk I decided to try something different and use a Prezi. Overall I think it went well.

Small data shock formation for QNLW PDF
On January 13 and 14, 2014, Gustav Holzegel and I gave a minicourse at the OXPDE Workshop on Nonlinear Waves and General Relativity, on the subject of small data shock formation for quasilinear wave equations. These are the slides.

Introductory notes on Sobolev spaces PDF
I gave a few introductory lectures on Sobolev spaces for the Cambridge Center for Analysis course on PDEs taught by Mihalis Dafermos in spring of 2011.

How to derive the Kerr metric by cheating quite a bit PDF
This came from a lecture I gave to MAT 451 at Princeton University on April 23, 2009. MAT 451 is a senior level mathematics course in which the instructor has great leeway in deciding what to teach. In 2009 my thesis advisor was in charge, and focused the discussion on mathematical aspects of general relativity. In this note I showed how one can start from the Schwarzschild metric, make an educated guess on an algebraic structure, and arrive at the Kerr metric.

Research papers
(Below is generated automatically from my author profile; they are sorted in order of most recent updates. Since I deposit all my research articles on the arXiv, the above link can give a slightly more pleasing browsing experience.)