Details of Grant 

EPSRC Reference:	EP/C535995/1
Title:	Surfaces, cobordisms & symplectic Floer homology
Principal Investigator:	Smith, Professor I
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Pure Maths and Mathematical Statistics
Organisation:	University of Cambridge
Scheme:	First Grant Scheme Pre-FEC
Starts:	01 July 2005	Ends:	30 June 2007	Value (£):	108,216
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
One of the oldest branches of topology is knot theory , the study of the possible ways loops of string can twist and knot in space. The research proposal involves studying analogous questions in dimension 4 rather than 3 -- and, partly because of intimate links to physics, 4-dimensional geometry is richer and more mysterious than geometry in any other dimension. The analogues of knots are now smooth surfaces which stretch between circles, much as soap films stretch between loops of wire. Soap films are minimal surfaces -- they stretch as taut as they possibly can, and have as little area as they can -- which in mathematical terms can be described by saying that the surfaces on which soap films lie must satisfy certain partial differential equations. Many mathematical objects satisfy such differential equations of physical origin -- heat equations, or equations describing motions of elementary particles in magnetic fields. Similarly, there are partial differential equations, governing other kinds of minimal surface ( holomorphic discs in a theory called Floer homology )l our intention is to apply these in a new way, to study the possible knottings of surfaces in four-dimensional space. Amazingly, despite the connections to physics and delicate analysis, often the underlying topological properties of these surfaces (analogous to whether a soap bubble has one region, or is split in two say) can be governed by quite formal algebraic laws (called Topological Quantum Field Theories ), and our hope is to better understand some of these underlying principles.
Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk Summary Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:
Further Information:
Organisation Website:	http://www.cam.ac.uk