| EPSRC Reference: |
EP/L01078X/1 |
| Title: |
The partition algebra: a new approach to the symmetric group and applications to P vs NP. |
| Principal Investigator: |
de Visscher, Dr M |
| Other Investigators: |
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| Department: |
Sch of Engineering and Mathematical Sci |
| Organisation: |
City, University of London |
| Scheme: |
Standard Research |
| Starts: |
30 June 2014 |
Ends: |
30 September 2017 |
Value (£): |
314,580
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
The Kronecker problem is a classical problem in Mathematics, which has been open for over a hundred years. It asks for a description of some coefficients, called the Kronecker coefficients, appearing in the representation theory of the symmetric group. More recently, this problem has been shown to play a key role in Geometric Complexity theory, an approach that seeks to settle the famous P vs NP problem.
We have recently proposed a completely new approach to the Kronecker problem using the duality between the symmetric group and the partition algebra. Early results suggest that this may well lead to a complete solution. This proposal aims at developing this tool further (and extending it to positive characteristics) to give a systematic study of the ordinary and modular representation theory of the symmetric group.
In parallel, we plan to liaise with the Computer Science community to investigate the implications of our work to the celebrated P vs NP problem.
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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 |
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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.city.ac.uk |