I am interested in category theory and its applications to the foundations of physics. I have developed categorical principles for reconstructing quantum theory based on a description of superpositions in category-theoretic terms.
More broadly, my 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:
- 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. From October 2014 - June 2018 I was a DPhil student in the Department of Computer Science at the University of Oxford, supervised by Bob Coecke and Chris Heunen. From August-October 2018 I was a Research Assistant in the School of Informatics at the University of Edinburgh. Since November 2018 I have returned to Oxford as a Postdoctoral researcher, as a recipient of an EPSRC Doctoral Prize.
Tensor Topology (Pre−print)
Pau Enrique Moliner‚ Chris Heunen and Sean Tull
A Categorical Reconstruction of Quantum Theory (Pre−print)
Quotient Categories and Phases (Pre−print)