Objective
Research objectives and content
The discovery of the Jones polynomial led to a renaissance in knot theory but was problematic in that it was not understood in terms of classical ideas. Vassiliev invariants give one way of relating the 'quantum' knot theory to pre-Jones knot theory and topology.
My intention is to continue my programme of understanding connections between Vassiliev theory and classical knot theory. The method will be by studying cabling operations on Vassiliev invariants. Cabling is a natural, classical operation on knots, and it is known that Vassiliev invariants behave reasonably well under cabling. Detailed study of this behaviour should reveal further insight into the algebraic structure of the Vassiliev invariants. It should also, for instance, allow the universal Vassiliev invariants of torus knots to be calculated.
The Alexander-Conway polynomial is a classically very well understood knot invariant; it appears to be related to cabling operations on Vassiliev invariants. I will closely examine this relationship to try to unveil further connections between classical and quantum notions.
Training content (objective, benefit and expected impact)
I will be working in a World-class mathematics department with active researchers in my own and also in closely allied fields: this will provide a stimulating atmosphere and a broad mathematical background for my mathematical development.
Links with industry / industrial relevance (22)
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
67084 Strasbourg
France
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