Objective
The research project is divided into several parts and includes scientific collaborations with A. Cattaneo (Zurich), R. Kashaev (Geneva), I. Korepanov (Chelyabinsk), and J. Porti (Barcelona).
- Connections between the volume conjecture and the volume form Rinat Kashaev and I are studying the connections between the non-abelian Reidemeister torsion for knot exteriors and the volume conjecture. The volume conjecture is currently a very active field of research and combines quantum invariants with hyperbolic geometry. The main objectives are the following. We are interested in obtaining new asymptotic expansions of certain specialization of the colored Jones polynomial for torus knots in terms of certain integrals with respect to the volume form constructed in my Ph.D. thesis. We next want to understand the geometrical meaning of the non-abelian Reidemeister torsion in such expansions. The case of hyperbolic knots will also be explored as a next step.
- Reidemeister torsion of geometric origin I am also beginning a collaboration with Igor Korepanov. The principal aim of this collaboration is to study connections between two different constructions of a knot invariant (and more generally for 3-dimensional manifolds) based on the theory of Reidemeister torsion. The main purpose of this collaboration is to establish some connections between Korepanov's invariant and a certain specialization of the torsion form that I define in my Ph.D. thesis. Moreover, we expect to obtain an algorithm (implemented on Maple) to explicitly compute this invariant for specific knots (e.g. 2-bridge knots).
- Integrability and integration of the volume form. We are interested in the computation of the integral of the volume form on the manifold of conjugacy classes of regular representations of the knot group. The objectives are to study the existence and to find methods of integration. This problem seems to be connected to the volume conjecture.
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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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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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
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-5
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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
BELLATERRA
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.