| EPSRC Reference: |
EP/Y016270/1 |
| Title: |
Computable manifolds |
| Principal Investigator: |
Douglas, Dr C |
| Other Investigators: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research |
| Starts: |
01 April 2024 |
Ends: |
31 March 2027 |
Value (£): |
536,092
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
This research programme will integrate expertise from Mathematics and Computer Science to develop theoretical and practical tools for the study of higher-dimensional topological and quantum-algebraic structures.
We will formulate a novel combinatorial and computable description of all possible singularities of manifolds, and leverage this model to give a complete finite classification of the stable singularities that can occur in spacetime dimension 4. We will then develop a corresponding combinatorial description, and spacetime-dimension-4 classification, of all possible non-singular deformations of manifolds. Combining the singular and non-singular descriptions, we will obtain the first faithful, finite, computable model of smooth spaces. Finally, using this model, we will develop and implement an efficient algorithm for producing an extensive dataset of such spaces, suitable for further theoretical and computational exploration.
This research effort will be organised into three strands---Higher singularities, Higher braids, and Combinatorial computable manifolds---and will be achieved by harnessing emerging frameworks and techniques at the cross-disciplinary intersection of quantum topology, quantum algebra, and combinatorial and computational topology.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |