I am applying to a PhD position in Pure math in UK.
Application form asks for research proposal but I don't have any specific problem now which I would like to work on although I have a good background on the specialization I want to pursue.
I emailed my prospective supervisor the following:
I was completing the PhD application form and now there is only Funding and research proposal left. Should I fill the research proposal at this stage? I mean, I want to work under your supervision in X but certainly I am not certain what exact problem I will work on.
The background I have in X and other branches of Mathematics (including Master’s Project) has been mentioned in my CV and Personal Statement.
I have been googling about it but I don’t think I can decide what exactly I should do about it. So, can you please guide regarding what exactly should I write in it or should I leave it blank? I shall be really thankful.
His reply was following :
I am not sure about exact the requirement here, but I don't think you are supposed to know exactly what to work on at this stage. I think just an indication of your research interests should suffice.
The issue I am facing is that I don't know what problem I should work on. I could write the title as "Topics in X" and I don't know what I can write in the abstract and other parts except the topics in X I have studied and my interest in particular branches of X. Pure mathematics is really specialized.
Can you please guide how should I approach the problem I am facing?