| EPSRC Reference: |
GR/S40817/01 |
| Title: |
Modular Invariant Theory of Finite Groups |
| Principal Investigator: |
Fleischmann, Professor P |
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| Department: |
Sch of Maths Statistics & Actuarial Sci |
| Organisation: |
University of Kent |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
22 September 2003 |
Ends: |
21 September 2006 |
Value (£): |
65,912
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Systems of polynomial equations describe geometric objects in a way, independent from our limited ability to visualize. Those properties which are independent of chosen coordinates are reflected in symmetries of the polynomials, the study of which is the main focus of invariant theory. While classical invariant theory mainly considered polynomials with complex coefficients, the focus of research has now shifted towards more general coefficient rings, in particular modular fields. The study of these modular invariant rings of finite groups is the main objective of this proposal. Recently the PI solved a long standing problem in constructive invariant theory (the 'Noether Gap') by developing a new reduction technique for invariants, which will allow to consruct new examples of invariant rings. New exciting connections between the structure of invariant rings and the structure of modular representations and cohomology have been discovered, that can be used to determne the depth of modular invariant rings. The depth measures the distance of a ring to be of Cohen - Macaulay type and is one of the most important parameters in modular invariant theory, but still very' difficult to compute. Now is the right time to combine the new techniques, developed by the PI and his collaborators, to progress towards a classification of modular Cohen - Macaulay invariant rings. This project offers a wide ranae of theoretical and consructive content. ideallv suited for a PhD - student.
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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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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.kent.ac.uk |