| EPSRC Reference: |
GR/M28903/01 |
| Title: |
ALGEBRAIC SOLUTIONS OF PAINLEVE EQUATIONS |
| Principal Investigator: |
Hitchin, Professor NJ |
| Other Investigators: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 July 1999 |
Ends: |
30 June 2002 |
Value (£): |
115,143
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Building on the accumulating knowledge about algebraic solutions to Painleve VI, which is currently emanating from various sources, the research aims to systematically attack the following problems: (i) determining for which values of the parameters a Painleve equation has algabraic solutions, (ii) attempting to derive methods of constructing them, (iii) using the symmetry group to classify them. The key to resolving the question may come from the special properties of a subgroup of the modular group of finite index which describes both the algebraic curve generated by an algebraic solution and the affect of the braid group in the isomonodromic interpretation. Some of the known methods of producing algebraic solutions rely on geometrical problems which are interesting in their own right. These deserve further investigation, and willbe undertaken within the program, but are unlikely to be exhaustive. Explicit algebraic solutions can be used to provide explicit solutions to a number of differential equations of current importance such as the Einstein equations in various forms and the WDVV equations for 2-dimensional topological quantum field theories, or equally to traditional questions in mathematics such as new systems of orthogonal coordinates.
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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 |