Details of Grant 

EPSRC Reference:	EP/C524063/1
Title:	Morse theory for the perturbed harmonic map equation and analysis on non-positively curved manifolds
Principal Investigator:	Kokarev, Dr G
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Mathematics
Organisation:	University of Edinburgh
Scheme:	Postdoc Res Fellowship PreFEC
Starts:	01 November 2005	Ends:	31 October 2008	Value (£):	115,007
EPSRC Research Topic Classifications:	Algebra & Geometry Mathematical Analysis Mathematical Physics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 14 Feb 2005 PDF Mathematical Sciences Sift 2004/05 Deferred
Summary on Grant Application Form
The research will deal with the harmonic map equations perturbed by lower order terms. This is an important class of nonlinear PDEs for mappings between manifolds and they often arise in varied questions in geometry and mathematical physics. The principal aims of the project are to develop Morse theory for the case when these equations are the Euler-Lagrange equations of the action functional perturbed by lower order terms and the target manifold is non-positively curved, to apply these results to the analysis and geometry of non-positively curved manifolds, to analyse applications and possible extensions of the techniques and results that will be developed to the theory of magnetic monopoles. In the latter theory only a few results are proved on the rigorous level so any progress in the area will be important.
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