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Details of Grant 

EPSRC Reference: EP/P023886/1
Title: Higher Categories for Compositional Computer Science
Principal Investigator: Vicary, Dr JO
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Computer Science
Organisation: University of Oxford
Scheme: EPSRC Fellowship
Starts: 01 December 2017 Ends: 30 November 2022 Value (£): 529,854
EPSRC Research Topic Classifications:
Fundamentals of Computing New & Emerging Comp. Paradigms
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
22 Feb 2017 EPSRC ICT Fellowships Interview Panel Feb 2017 Announced
12 Jan 2017 EPSRC ICT Prioritisation Panel Jan 2017 Announced
Summary on Grant Application Form
In this proposal I outline a bold programme of research, which seeks to take new ideas in modern mathematics and apply them to open problems in a broad range of areas: quantum information, automated reasoning and abstract algebra.

These problems are connected together by a common idea: composition. When individual structures combine to form a single system, how can the behaviour of the whole be predicted from the behaviour of the parts? Modern mathematics offers a range of new and exciting tools, together referred to as category theory, to study compositional behaviour in a direct and powerful way. These will provide the main techniques for my research.

In this fellowship proposal, I propose to use these ideas to achieve significant breakthroughs across a broad range of areas of modern science, asking questions such as: how do quantum computational structures compose? What is the financial value of a composite financial instrument, or the biological behaviour of a composite cellular structure? What is the combinatorial structure of an intricately-knotted higher-dimensional manifold? What are the fundamental computational structures that would allow machines to model these systems and predict their behaviour, either running automatically, or guided by a scientist?

This research project combines applied work in a number of application domains with the development of computational tools, unified by mathematical ideas of the most pure and abstract form. My track record establishes my ability to deliver such a varied and inter-disciplinary research programme, to publish the results in high-impact venues, and to influence the broader academic community.
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Organisation Website: http://www.ox.ac.uk