I did a PhD in Maths, and I wrote a few research papers while I was doing it, as well as a few things which I used for various outreach projects I was involved in - both the Art of Maths summer school, which gave gifted sixth form students an introduction to university level mathematics and some one-off talks I gave at various schools around London.

You can find some of my research here.
You can find some of the outreach stuff I did here.