| EPSRC Reference: |
GR/A90258/01 |
| Title: |
PLEATING INVARIANTS:HYPERBOLIC GEOMETRY,FRACTAL LIMIT SETS AND PARAMETER SPACES OF KLEINIAN GROUPS |
| Principal Investigator: |
Series, Professor C |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Senior Fellowship (Pre-FEC) |
| Starts: |
01 October 1999 |
Ends: |
30 September 2004 |
Value (£): |
242,178
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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A Kleinian group is a group of matrices with complex coefficients which simultaneously defines a geometrical structure on 3 dimensional hyperbolic space, a fractal limit set in the plane (analogous to Julia sets in complex iteration), and one or more Riemann surfaces (quotient of the limit set complement by the group). Changes in the matrix parameters are reflected in changes in the fractal patterns, in the surface structures (Teichmuller theory), and in the spatial geometry. The interplay between these effects is, however, notoriously hard to control. Pleating invariant theory, originated in 1988 by C. Series and L. Keen, pointed out hitherto unobserved geometrical relationships giving new insights into this problem. It has dramatically increased our ability to compute parameter spaces (analogous to the Mandelbrot set and important for fractal graphics). Developments will provide a powerful systematic tool for mathematical exploration and computation. Beautiful fractal limit sets, reminiscent of seahorses and fine lace, will be publicised and possibilities for commercial design explored.
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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.warwick.ac.uk |