Constructing knotted fields
Benjamin Bode (University of Bristol)
Howard House, 4th Floor Seminar Room
The term 'knotted fields' can refer to many different physical systems, an electro-magnetic field with knotted field lines, knotted vortex lines in a scalar optical field or a fluid, knotted disclination lines in a liquid crystal and many more.
Despite this diversity the problem of finding a mathematical description of such a system which contains a given knot K almost always reduces to finding a polynomial ℝ³ → ℂ that vanishes exactly on K.
In this talk I am going to present an algorithm that for any given knot K constructs such a polynomial, whose degree can be bounded in terms of topological data associated with K, allowing us to theoretically construct knotted fields with arbitrarily complex knots.
Please contact M.Gradhand@bristol.ac.uk for further information.