Upcoming PhD interview 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?
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!