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Dr Jonathan Gorard

Dr Jonathan Gorard

Researcher and Teaching Associate

Room 1.25, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG


I'm a mathematician by training, but I'm interested very broadly in the interface between abstract computation and the foundations of physics and mathematics. In particular, much of my present research focuses on the application of category theory, topos theory and certain aspects of theoretical computer science to a diverse range of problems, including algorithmic models for the structure of spacetime, compositional foundations for quantum computation, higher-order type theories and the automation of mathematical reasoning, algebraic and compositional semantics for graph rewriting, etc.

I run a small, multi-disiplinary and geographically-distributed research group working on applying the abstract principles of compositionality and functoriality to a variety of topics in science and technology. My published research comprises topics ranging from general relativity and quantum information theory to computational complexity theory and homotopy type theory, and has previously been showcased in publications including Forbes magazine, Wired magazine and Scientific American.


Before coming to Cardiff, I was previously a master's student, PhD student and researcher at the University of Cambridge, focusing on numerical aspects of hyperbolic partial differential equations; I remain a senior (non-resident) member of King's College, Cambridge. I have also been a research fellow and consultant mathematician at Wolfram Research, Inc. since 2017, leading advanced algorithms R&D projects relating to automated theorem-proving, symbolic logic, semantic representation of pure mathematics, quantum computation, discrete-state quantum mechanics, (hyper)graph rewriting, non-deterministic computation, category theory and many other topics. I'm also one of the co-founders and former associate directors of the Wolfram Physics Project.

I'm a regular contributor to various seminar groups and workshops on applied category theory (and other allied topics) across the UK, the US and Europe, including the Graph Transformation Theory and Applications group at the University of Paris, the ZX-Calculus group at the University of Oxford, the General Relativity group at the University of Cambridge, the Mathematically-Structured Programming group at the University of Strathclyde and the Topos Institute in Berkeley.


I support undergraduate and postgraduate teaching across a range of modules in the Schools of Mathematics, Physics & Astronomy and Computer Science & Informatics, with a particular focus on scientific computation, computational mathematics and theoretical computer science (especially algorithms, data structures and programming paradigms).

I also run two short extra-curricular lecture courses, namely Category Theory for Multicomputation and Computational Physics & the Wolfram Model, for any students (and others) who are interested in these areas of current research.


Research links