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Details of Grant 

EPSRC Reference: EP/K00591X/1
Title: Knot homology: theory and computation.
Principal Investigator: Lobb, Dr A J
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematical Sciences
Organisation: Durham, University of
Scheme: First Grant - Revised 2009
Starts: 10 March 2013 Ends: 09 June 2014 Value (£): 89,409
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
18 Sep 2012 Mathematics Prioritisation Panel Meeting September 2012 Announced
Summary on Grant Application Form
Knots to mathematicians are equivalent to what they are in real life: tangled up pieces of string. To a topologist it doesn't matter if you move the string around in space, so long as you keep the endpoints of the string fixed and you don't use your scissors! In order to distinguish between different knots, topologists compute quantities that don't change as you move the string around.

The research supported by this grant studies a particular class of these quantities (knot homologies) that have been discovered within about the last ten years. In doing this research we aim to prove theorems distinguishing between various knot homologies, and also carry out explicit computational work to understand better the structure of these theories. Interestingly, there are intimate connections of these theories with physics (gauge theory and string theory) so that we expect our research to have relevance even outside the realm of pure mathematics.
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