I applied for some PhD's in differential geometry in the UK, and I was offered an interview this coming Wednesday and they said this in the confirmation email:

"The interview will be conducted by insert prof name and myself and should last around 30 minutes In the interview we will ask about relevant courses you have taken, we will explore your knowledge and understanding of these courses, and we will discuss your motivation in applying for the insert department name PhD. We will also ask some technical mathematical questions about topics you have covered."

Any clues what I should expect and how I should prepare? How much can they rip me apart in 30 mins?

It’s also worth noting that I did my undergrad in theoretical physics; would this imply that the technical questions refer to undergraduate questions or to the Masters programme I’m currently enrolled in (which allows me to study both pure and applied maths)?

Furthermore would the relevant courses taken mean the ones I’m attending currently for my Masters programme (given I did submit a list of the courses I attended last term and the ones I’m attending this term) or, again, would it refer to stuff I have independently studied in my undergraduate, which was a point I mentioned in my application?

  • 2
    I can't help with a UK relevant answer, but suggest that you honestly admit that you don't know the answer when you don't.
    – Buffy
    Jan 24, 2020 at 1:41
  • It's a bit tricky to answer the broader questions without knowing specifics (and of course you probably won't want to go into detail on this site). For what it's worth: given that the context of this question implies you are not currently studying in the UK, I expect that the people reading your PhD application may feel unsure about what is and isn't covered in the courses listed in your transcript. They may also not be familiar with the education system of the country where you're currently studying, if it's not the UK. So they want to find out what diff geom you know
    – Yemon Choi
    Jan 24, 2020 at 2:26
  • (I say this as someone who has in the past been involved in this kind of interview)
    – Yemon Choi
    Jan 24, 2020 at 2:27

2 Answers 2


Any clues what I should expect and how I should prepare? How much can they rip me apart in 30 mins?

My number one tip: don't go into it expecting to be ripped apart, they're academics, not leopards! :)

Seriously, though, every PhD interview I had (UK, cosmology, three years ago) was very friendly and relatively informal. Some were more informal than others, and I think it's no coincidence that I accepted the offer from the place where I had the most relaxed interview experience. Remember that not only are the interviewers looking to see if you're a good fit, you need to find out if the department is a good fit for you. I highly recommend talking to their current PhD students if you get a chance!

Since they say in their email that they will ask about relevant courses, think about which of the courses you've taken are most in line with the PhD project(s) you're applying for. The technical questions I was asked were all closely related to cosmology, even though I'd taken courses on solid state physics, electromagnetic theory, a whole bunch of solar physics courses... you get the picture. At the time I didn't have a strong cosmology background so I didn't know the answers to quite a lot of things, but I used my general physics knowledge to try and reason things through, explained what I was thinking and was honest when I didn't know the answer. They're not expecting you to know everything about your topic of interest already, they're far more interested in seeing how you think and communicate.

However, the majority of all the interviews I had focused on the research I was doing for my Master's dissertation. I talked about my work in detail, as well as the relevant literature. I think my ability to discuss the basic ideas in a very recent paper that was relevant to my project (and also why I didn't completely agree with it) left a good impression with the panel. If you've done any kind of research project or dissertation before, expect to spend a lot of the interview talking about it, so make sure you know it inside out.

In summary:

  • Look forward to the interview as a chance to discuss your subject with experts, and to look around a new department.
  • Be prepared to stand at the whiteboard and explain your work and thinking (practice doing this with a friend if you haven't done it before, good communication is key).
  • Know your subject well and have a good idea of the relevant literature to the projects you're applying for.

Good luck!


I am a first year PhD student in theoretical computer science (formal methods), which is close enough to math that I think my experience my be relevant. (Also my undergrad is in math.). When I applied to programs I did multiple interviews like this. In my experience the technical questions pertained to:

  • literature written by or related to the work of the professor I applied to work with;
  • potential research topics;
  • my academic background and coursework.

Other than Oxford in the UK all my interviews were in the US so this may differ country by country but I suspect the following:

  • any courses you have taken in any previous degree are open for discussion;
  • any research topics you have studied in the past or worked on professionally are open for discussion;
  • research topics and literature pertaining to the professor you might work with will almost certainly be discussed.

As such, my best advice is to read papers by the professors you want to work with, and read some of the papers they cite. If you can explain a result to the interviewer and show how this relates to your own interests it will go a long way.

My experience was that these were not like job interviews - they were not very intimidating. However this might be different in the UK. I felt like my knowledge of academic literature was very useful in these interviews, but my knowledge of specific mathematical or computational facts was not. For example, I was not asked to define a Buchi automaton or solve a differential equation or do a whiteboard programming exercise, but I was asked to explain some results from various papers and how they related to my interests.

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