Q. Are you taking students next year?

A. I am always interested in the possibility of taking on talented students wishing to study for the D. Phil degree at Oxford (called a PhD in almost all other universities) under my supervision.

Q. How do I apply?

A. All students must apply through the formal process, full details of which may be found here. You should aim to meet the first deadline, which is near the start of January each year. In addition to the formal application, I welcome informal approaches from prospective students by email, which might lead to a short informal chat via Teams or Zoom. However, such an approach is not necessary and if you prefer to simply submit a formal application, that is fine. Shortlisted candidates for the D. Phil are interviewed by Teams or Zoom.

Q. What projects do you have?

A. I maintain an open mind regarding what project a student might work on. In the past, I have had students arriving thinking that their interest is in combinatorics, but ending up writing papers in analytic number theory. I have supervised theses across a broad range of topics from quite classical analytic number theory, through additive combinatorics, to more algebraic topics bordering on group theory, as well as topics related to ergodic theory. The papers of my current and former students may be accessed from this page. In recent years my interests have been rather more in the direction of number theory (additive and analytic) than combinatorics.

If you are potentially interested in working with someone, I would recommend that you take a look at the abstracts of some of their more recent papers. This is, of course, a good way to find out what sort of things interest them. My papers are all freely available on the arxiv via this link.

I like students to get stuck into research straight away, picking up necessary theory as they progress rather than taking the first year or two learning things. Thankfully, the nature of the subject allows this. I would typically suggest a couple of problems to begin with, but encourage students to follow their interests and explore any ideas that come up independently. The aim is to become fairly independent in research by the end of your time here.