I am willing to supervise PhD students interested in topological quantum field theory, enriched category theory, metric spaces and other related topics.
If you are interested in applying to work with me you should send me an email (telling me you've read this information!). I will probably suggest you put in a formal application to the department so that you are in the system and can be considered for funding.
You should read carefully the SoMaS information on PhD places, in particular the information on funding opportunties and deadlines. As it explains on those webpages, if you wish to apply for funding you will have to email maths-phd@sheffield.ac.uk with the subject "PhD funding application" after filling in the university application form.