Details of Grant 

EPSRC Reference:	GR/T01617/01
Title:	Moduli Spaces of Stable Curves: their Cohomology via Geometric Invariant Theory
Principal Investigator:	Kirwan, Professor FC
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematical Institute
Organisation:	University of Oxford
Scheme:	Senior Fellowship (Pre-FEC)
Starts:	01 April 2005	Ends:	31 March 2010	Value (£):	302,782
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 26 May 2004 Fellowships Central Allocation Panel Deferred 12 Mar 2004 Maths Fellowships Sifting Panel 2004 Deferred
Summary on Grant Application Form
The study of complex algebraic curves, and how they vary in families, has been fundamental to algebraic geometry for at least the last century. Huge advances have been made in recent decades, and unexpected but extremely important links with theoretical physics and other parts of mathematics have been discovered. Nonetheless, in spite of 150 years of investigation, our understanding of the topology of the moduli spaces of curves is still very incomplete. The aim of this project is to gain new understanding of the topology of these and related moduli spaces by representing them as quotients in the sense of geometric invariant theory and applying methods developed over the last twenty years for studying such quotients.
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Organisation Website:	http://www.ox.ac.uk