I spent a couple months this summer doing a very enjoyable research project supervised by Martin Hyland, looking at several topics to do with algebraic theories. It was a great opportunity to get some idea of what research can be like, and to learn from someone with much more experience.

I recently gave a short talk about the project, and I’ve uploaded the slides. The talk was aimed at mathematics students who don’t know any category theory, so rather than taking a category-heavy point of view, I instead spent the first half explaining equational theories in some detail, while in the second half I tried to give a more intuitive description of the problems that I was actually working on.