I work in a new area of research called derived bornological geometry, proposed by Ben-Bassat, Kelly, and Kremnizer. The aim to is provide a workable theory for derived analytic and derived smooth geometry using simplicial commutative complete bornological rings. My current research is focused on studying derived moduli stacks in these contexts. Some expository talks about this can be found in the Talks tab of my website.
Publications
Koszul Monoids in Quasi-abelian Categories, Journal of Applied Categorical Structures, 31(50), 2023, journal link, arXiv link
Preprints
A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs, 2026, arXiv link
A Representability Theorem for Stacks in Derived Geometry Contexts, 2024, arXiv link, submitted
DPhil Thesis
A copy of my DPhil Thesis, titled Stacks in Derived Bornological Geometry, is available here. This includes the content of the papers `Koszul Monoids in Quasi-abelian Categories' and 'A Representability Theorem for Stacks in Derived Geometry Contexts', along with a very early draft of 'A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs'.
Other Projects
Part B Extended Essay - A categorical approach to subgroups of quantum groups and their crystal bases - supervised by Professor Kobi Kremnizer - expository paper available here
A literature review I did for the Oxford Topology Advanced Class on Six Functor Formalisms - A Review of Six Functor Formalisms for Higher Stacks - available here