Doing a DPhil in Analytic Topology

The Formalities

Most DPhil students start in Oxford in Michaelmas Term, which usually starts at the beginning of October. It is entirely possible to start in other terms, although it will require slightly more organisation.

In all cases you need to apply early, especially if you require funding from Oxford sources. There are regular graduate open days in the Mathematical Institute, which are worth attending. Most Oxford students who want to stay here for their DPhil, apply just after the Christmas holidays, i.e. January or early February. It is possible to apply later, but it will be harder to obtain College accommodation or funding.

Before you apply, please get in contact with pjcoll [-at-] maths [dot] ox [dot] ac [dot] uk"> Dr P J Collins. He can advise you on how to apply, which forms to fill out and how the process works.

Your First Term

During your first term you will most likely do a 'theorem sequence'. Depending on how much topology you have done before, this will consist of known theorems which you are asked to prove (of course without looking them up in the literature). Compared to the typical problem sheets you will not be led through the question, but have to come up with the necessary intermediate results yourself.

The aim of the theorem sequence is threefold. Firstly, you will learn a lot of new and advanced topology. Secondly, it is the first step in discovering and proving theorems yourself, so you can think of it as a gentle introduction to doing research. And lastly, it will allow you to explore various areas of topology, so that you can develop a preference in which of these you would like to work in.

Where To Go From There

Towards the end of the first term or the beginning of the second term, your supervisor and you will most likely be thinking about a first problem to try. In every subject in mathematics it often is the case that this first problem will prove too hard and you will feel that you are not getting anywhere. One of the advantages of analytic topology is that most areas require only a few weeks of reading to reach the border of current knowledge. Thus it is easy to switch to a different problem or at least give your first problem an entirely new twist.

How to Find a Good Problem

In every mathematical subject, there are two major sources of problems: people and papers. What makes analytic topology different is that there is a third source, namely the book 'Open problems in topology' which is updated regularly. Some of the problems in there will look obscure, some of them will seem very hard, but one of us or someone who is in regular contact with the analytic topology group, will probably be able to bring the problem to live.