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.

A converse to Banach's fixed point theorem, due to Bessaga, is discussed.
Last updated on 5 min read expository

We explain how to conformally compactify pseudo-Euclidean spaces with $(p,q)$ signature.
Last updated on 4 min read expository

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

Expository note on the Runge phenomenon
Last updated on 1 min read expository

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

In a first course in differential geometry/topology we are often taught the following version of Sard's theorem: Theorem   …
Last updated on 9 min read expository

We show that trapped surfaces cannot exist in (2+1) dimensional relativity.
Last updated on 8 min read expository

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

Life is boring in low dimensions.
Last updated on 3 min read expository

The relationship between gravitational red shift and the surface gravity of black holes is explained.
Last updated on 2 min read expository