So you are thinking about doing a PhD with me? I appreciate that applying for a PhD is a difficult and somewhat mysterious process for many students. Indeed, I made some mistakes when I applied to do a PhD myself. So I wanted to write down some advice for people that may be interested in applying to do a PhD with me.
Decisions about PhD applications are done centrally and not by individuals like myself. The only way to get accepted as a PhD student is to follow the application process described here.
I have written down the following ideas for PhD projects:
However, these are not the only topics that I am interested in and that I could supervise a PhD project in. You can have a look at my publications to find out what topics I have worked on. At the end of many research papers, there is a section with ideas that could form the basis of a research project.
Think about your interests and your background and use this to be selective in the places and supervisors that you apply with. I realize that it is hard at the end of your undergraduate program to decide which area of mathematics you like best (even now I find this question hard to answer!), but it is worth your effort to reflect on this and try to formulate a tentative answer, at least for yourself.
Here are some questions for you to consider:
When considering applications, I expect students to have some research experience. This does not have to be original research because the point of doing a PhD is that you learn how to do original research, but I do expect you to have done a project or a thesis or something like that. I also expect some knowledge of mathematical analysis (including proofs), numerical analysis and programming.
I will look at your degree transcript and project report or thesis for evidence. If you have relevant experience from outside your formal university education, you should say so.
I do not expect you to include a detailed research project proposal in your application. Instead, explain what research direction you would like to work on. See the second and third bullet point above for some ideas.
For more information about doing a PhD in mathematics at the University in Leeds, see our page on research degrees.
If you have questions about the application process, contact the MAPS PGR Admissions Office.
If after this you are still interested in doing a PhD with me, it may be a good idea to ask me some questions. I will be happy to answer your questions over email, or we can arrange a meeting, either online or face-to-face.
Finally, here is some useful general advice written by others: