EPSRC Reference: 
EP/F006705/1 
Title: 
Derived categories of coherent sheaves on hyperkahler manifolds 
Principal Investigator: 
Thomas, Professor R 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Imperial College London 
Scheme: 
Standard Research 
Starts: 
05 October 2007 
Ends: 
04 May 2008 
Value (£): 
39,904

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Physics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
06 Jun 2007

Mathematics Prioritisation Panel (Science)

Announced


Summary on Grant Application Form 
Algebraic geometry, and particularly the geometry of HyperKahler manifolds, studies a highly constrained type of geometry which is very rigid with very few global symmetries. Mysterious predictions coming from dualities in string theory in physics, however, relate these spaces to symplectic manifolds: these are much more flexible geometries with many symmetries. (For instance the symmetry groups of low dimensional topology  braid groups, mapping class groups  occur as the symmetry groups of many symplectic manifolds.) The reason is that while the symmetries do not act on the HyperKahler manifolds themselves, they act on their categories of Dbranes .This connection between algebraic geometry and low dimensional topology is a surprise and allows one to use the sophisticated and deep structures of algebraic geometry to construct invariants in low dimensional topology  i.e. algebrogeometric data encoding properties of the low dimensional topology that can be used to distinguish different topologies or shapes . The simplest example is to produce knot invariants from algebraic geometry, giving data which can distinguish between knotted loops of string embedded into normal 3dimensional space in different ways.

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Summary 

Date Materialised 


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Further Information: 

Organisation Website: 
http://www.imperial.ac.uk 