Who used a “pure maths” theorem this week in their work?

I often get requests from my students for more examples of the uses of “pure” mathematics in other areas. Of course one possible answer is “it’s all mathematics anyway” and another is “that’s not why I do pure maths”. Then there are all the standard things such as applications of Number Theory in cryptography and internet security, and countless applications of linear algebra. But somehow I would like to have some other kinds of answers along the lines of “I used this theorem last week to help me with this real-world topic”. For example, I was able to use a standard theorem about uniform continuity to clarify a technical detail for my colleague Daniele Avitabile in his recent paper about neural nets (see https://arxiv.org/pdf/1603.04486v1.pdf), even though I know nothing about neural nets.

I would quite like to give more examples of this sort of thing. So, who used a “pure maths” theorem in their work this week?

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