Interview for postdoc position in mathematics I have an interview for a postdoc position in Mathematics at a very good university in the UK. The interview committee comprises a maths professor (not in my field, which is analysis of PDEs) and three other professors from other scientific disciplines. 

I do not expect any technical questions since they are not in my field. But I am worried they will ask me: "why is your work important/useful/relevant?" in the context of applications to real-life. What can I say in such a situation? Also does anyone have any general advice to what such a panel might ask me?
Why should you be worried? This is a pretty standard postdoc position interview question and you should be prepared to answer it. 

I echo P.Windridge's comment:- your specific answer may be less important than a clear indication that you've considered how your research fits in, extends, challenges, tests the current state of the art in your field. 

You've set the problem of answering this question in the context of "real life", whatever that is. For your specific case, I would have thought the "real life" applications of PDEs is easily referenced.