Published a graduate textbook on category theory and quantum computation (Oxford University Press)
Proposed a new definition of strictly unital ∞-categories (LICS2022#P36)
Gave the first general definition of strictly associative ∞-categories (arXiv:2109.01513#P39)
Created homotopy.io, a graphical proof assistant supporting composites and homotopies in arbitrary dimensions with advanced visualization (LICS2022#P41, LICS2019#P36, LICS2017#P29)
Showed the word problem for monoidal categories is solvable in quadratic time (LMCS2018#P34)
Proved the word problem for braided monoidal categories is at least as hard as the unknot problem (ACT2021#P40)
Defined quantum Latin squares (QIC2015#P17, QIP 2016)
Unified definitions of unitary error bases and quantum Latin squares as biunitary vertices in 2-Hilbert spaces (LICS2012#P8, QIP 2017)
Background
Professor of Future Computation at the Computer Laboratory, University of Cambridge
Royal Society University Research Fellow
Fellow of King's College, Cambridge
Research aims to develop new logical and structural techniques to transform future computation in quantum and classical domains
Extensively uses category theory to understand how interacting systems process information
Also interested in advancing category theory itself to make it more powerful and accessible
Member of the Cambridge Logical Structures Hub (CLASH) research group
Welcomes undergraduate, Master's, PhD students, and postdoctoral researchers to join his team