I am interested in category theory and its applications to the foundations of physics. Most recently, I have developed categorical principles for reconstructing quantum theory (to appear soon!) based on a description of superpositions in category-theoretic terms.
More broadly, my (upcoming) thesis explores the categorical study of operational theories of physics. This draws connections between the field of generalised probabilistic theories and categorical approaches such as categorical quantum mechanics and effectus theory. For the origin of these ideas see the pre-print Operational Theories of Physics as Categories. (video, slides).
Other work on categorical approaches to physics includes:
- An account of spatial features in monoidal categories with Chris Heunen and Pau Enrique Moliner
- A pictorial proof of security of quantum key distribution with Aleks Kissinger and Bas Westerbaan
- The emergence of the classical from the quantum with Bob Coecke and John Selby.
I am also intrested in pure category theory. With Chris Heunen I have studied appplications of monoidal methods from physics to general categories of relations (video, slides), and particularly those of Mal'tsev categories.
My undergraduate and masters degrees were in Mathematics at the University of Cambridge.
Quotient Categories and Phases (Pre−print)
Condition for an n−permutable category to be Mal’tsev
In Cahiers de Topologie et Géométrie Différentielle Catégoriques. 2017.
Space in Monoidal Categories
Pau Enrique Moliner‚ Chris Heunen and Sean Tull
In Proceedings of Quantum Physics and Logic (QPL). 2017.