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EPSRC Reference: GR/R32055/01
Title: Determining the depth of Modular Invariant Rings
Principal Investigator: Fleischmann, Professor P
Other Investigators:
Shank, Dr RJ
Researcher Co-Investigators:
Project Partners:
Department: Sch of Maths Statistics & Actuarial Sci
Organisation: University of Kent
Scheme: Standard Research (Pre-FEC)
Starts: 13 August 2001 Ends: 12 September 2001 Value (£): 1,968
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
Systems of polynomial equations describe geoemetric 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 theme of invariant theory. While classical invariant theory of finite groups mainly considered polynomials with complex coefficients, new applications in geometry and topology call for results, valid for modular fields whose characteristic divides the group order. In this situation invariant rings are not necessarily Cohen - Macaualay rings. The degree to which this fails is measured by the 'depth' of the invariant ring. Determining this depth is one of the most interesting but also difficult tasks in modular invariant theory. New methods for this problem have emerged recently in the work of the two investigators at Kent and the proposed visiting fellow.A joint effort to combine these techniques in a direct cooperation at Kent is the best forward to achieve further breakthroughs in determining the depth of invariant rings.
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Organisation Website: http://www.kent.ac.uk