Project description
Tracking the time evolution of knots in electromagnetism and quantum mechanics
Knot theory, the study of closed curves in three dimensions, and their possible deformations without one part cutting through another, is increasingly important in biology, chemistry and physics. Funded by the Marie Skłodowska-Curie Actions programme, the KNOTDYNAPP project aims to study the time evolution of knots in different dynamical systems. Special focus will be placed on proving the existence of differential equation solutions that contain knots that persist for all time in electromagnetism and quantum mechanics. To address certain mathematical problems in these fields, researchers will borrow techniques from differential geometry and low-dimensional topology.
Objective
Mathematical knot theory plays an increasingly important role in biology, chemistry and physics. In this project we aim to study the time evolution of knots in different dynamical systems. We are particularly interested in differential equations that are motivated by electromagnetism and quantum mechanics. For such differential equations we aim to prove the existence of solutions that contain knots, which evolve as desired, and explicitly construct such solutions.
In the case of electromagnetic fields this refers to vector fields, representing the electric and magnetic part of such a field, that satisfy Maxwell's equations and have closed flow lines in the shape of a given knot for all time. In particular, we want the knot type of this closed flow line to be stable, i.e. it is not allowed to change over time.
In the case of quantum wavefunctions we are concerned with complex-valued functions that satisfy linear or non-linear Schrödinger equations and whose nodal set is knotted at a moment in time. We plan to develop a construction of such functions for which the time evolution of such a quantum vortex knot is determined by a prescribed surface, embedded in 4-dimensional space representing space and time.
We also study relations between topological properties of knots and the corresponding functions. For example, we investigate the connection between the fibration property of a knot K and the non-vanishing of a magnetic field induced by an electric current through a knotted wire in a shape that is isotopic to K.
These mathematical problems are approached with techniques from differential geometry, low-dimensional topology and the theory of differential equations. The proposal also discusses the two way transfer of knowledge between the host institute and the candidate.
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.
- natural sciences physical sciences electromagnetism and electronics electromagnetism
- natural sciences mathematics pure mathematics topology knot theory
- natural sciences mathematics pure mathematics mathematical analysis differential equations
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics topology algebraic topology
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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)
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.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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.
(opens in new window) H2020-MSCA-IF-2020
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
28006 MADRID
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.