Constructing knotted fields

13 October 2017, 2.00 PM - 13 October 2017, 3.00 PM

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 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.

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