Details of Grant 

EPSRC Reference:	GR/S71200/01
Title:	Algebraic geometry over groups & algorithms for Artin Groups
Principal Investigator:	Duncan, Dr A
Other Investigators:	Howie, Professor J Gilbert, Dr ND Borovik, Professor A Rees, Professor SE
Researcher Co-Investigators:	Dr M Batty Dr E Esyp Dr C Rover
Project Partners:
Department:	Mathematics and Statistics
Organisation:	Newcastle University
Scheme:	Standard Research (Pre-FEC)
Starts:	14 October 2003	Ends:	13 January 2004	Value (£):	8,721
EPSRC Research Topic Classifications:	Algebra & Geometry Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Equations in groups maybe defined just as equations over integers reab or any other ring. The lack of ring structure can however make such equations very difficult to manipulate & solve. Much work has been done in the last 20 years & recently a framework of Algebraic Geometry over groups has been developed (by amongst others one of the proposed visitors). The current project aims to characterise certain basic solution sets to equations in such a way that it is easy to recognise which sets are solution sets & to which equations they correspond. We shall build on work carried out by our visitors in Free groups. In relation to this work various algorthmic propoerties of the classes of groups studied will be developed.
Key Findings
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Organisation Website:	http://www.ncl.ac.uk