My maths work can broadly be classified as “categorical geometry”. Have a look at my papers on arXiv if you don’t believe me.

## Derived geometry and higher categories

This project is about developing the foundations of derived geometry and stack theory in a way that’s agnostic to the underlying “underived” or “smooth” geometry. In particular, I want a framework for derived differential geometry robust enough to support certain popular compactified moduli stacks of solutions to elliptic PDEs, with an eye to describing topological field theories. To realise this goal, I’ve had to get back to basics and revisit various foundational aspects of $\infty$-category theory and its cousins....