Maths

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....

My thesis and a few years of postdoctoral work were centred around developing a “scheme-theoretic” basis for tropical geometry. My fundamental motivating examples came from the skeletons of Berkovich spaces. Skeletons of non-Archimedean analytic spaces It is related to various things, including: Kato fans for log schemes Tropical varieties associated to subvarieties of tori Skeletons Affine manifolds with singularities as used in the Gross-Siebert programme. Q. “Skeleta” or “skeletons”?...