Details of Grant 

EPSRC Reference:	GR/S44136/01
Title:	Isomonodromic deformations, tau functions and matrix models
Principal Investigator:	Hitchin, Professor NJ
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematical Institute
Organisation:	University of Oxford
Scheme:	Standard Research (Pre-FEC)
Starts:	01 April 2003	Ends:	30 June 2003	Value (£):	7,867
EPSRC Research Topic Classifications:	Algebra & Geometry Mathematical Physics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Isomonodramic deformations appear in many parts of geometry and theoretical physics. In general the equations cannot be solved explicitly an rise to Painleve transcendants, but algebraic or hypergeometric solutions seem to play a special role. For Painleve VI, the geometry of the D4 I diagram governs these solutions - it is proposed here to investigate the structure for more general systems. In a separate strand, the recent we Dijkgraaf and Vafa has brought the tau function for matrix models into a central role in supersymmetric Yang-Mills theory and Calabi-Yau manifolds string theory. It is proposed to investigate the systems lying behind this, which may involve the use of the twistor-theoretic tau function and the consideration of systems with singularities of a higher order than have been considered hitherto.
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Organisation Website:	http://www.ox.ac.uk