Expository

This is a collection some of the expository notes that I have written, they range in topic, some closer to my research and some farther away. As opposed to posts in "Mathematical Diversions", posts here are intended to be read by other people. I welcome comments and corrections.

About the Einstein-Infeld-Hoffmann theorem characterizing geodesics.

The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …

Expository article on the geometric notion of derivatives.

A converse to Banach's fixed point theorem, due to Bessaga, is discussed.

We explain how to conformally compactify pseudo-Euclidean spaces with $(p,q)$ signature.

Lecture slides that Gustav Holzegel and I used for the January 13-14, 2014 OXPDE Workshop at Oxford University.

Expository note on the Runge phenomenon

Lecture notes introducing Sobolev spaces.

In a first course in differential geometry/topology we are often taught the following version of Sard's theorem: Theorem   …

We show that trapped surfaces cannot exist in (2+1) dimensional relativity.