| EPSRC Reference: |
EP/Z535333/1 |
| Title: |
Cohomology, Geometry, Explicit Number Theory |
| Principal Investigator: |
Sengun, Dr M |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Department: |
Mathematics and Statistics |
| Organisation: |
University of Sheffield |
| Scheme: |
Other JeS Guarantee Calls TFS |
| Starts: |
01 December 2024 |
Ends: |
30 November 2028 |
Value (£): |
267,922
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Summary on Grant Application Form |
The aim of COGENT is to develop, analyze and apply efficient algorithms in three core areas where computer algebra plays an
important role: Cohomology, Geometry and Explicit Number Theory. These will have applications to a broad range of mathematical
problems, and will touch as well upon related topics like cryptography and quantum computing. Such applications of mathematics
are expected to have a wide-ranging impact on economic and societal problems. Recent years have seen a plethora of high-flying
projects and a dazzling variety of applications of methods in computer algebra. One of the emerging challenges is to combine ideas
of different areas of computer algebra, to share expertise between them, and to educate young researchers in theoretical and
practical methods with a focus of transferring knowledge and training software development skills. COGENT provides an innovative
training program to facilitate this and has ambition to stimulate interdisciplinary knowledge exchange between number theorists,
algebraists, geometers, computer scientists and industrial actors facing real-life challenges in symbolic computation in order to
bridge key knowledge gaps. This will address the urgent need for computer assisted investigations of several longstanding
conjectures in mathematics, and EU industry's need for workers with an advanced mathematical and computational skill set. Not only
do we expect to merge the best known tools for these purposes with innovative approaches and ideas to extract previously
inaccessible cohomological information of the underlying arithmetic groups, but we also anticipate finding new hitherto unknown
concepts as we intend to enhance the currently available data pool by a whole order of magnitude. The latter will allow the
researchers to find hidden patterns, with the ambition to form a solid basis for formulating novel cornerstone conjectures, ideally in
the spirit of the famous Million-Dollar Birch and Swinnerton-Dyer Conjecture.
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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.shef.ac.uk |