Benjamin Bode


Constructing knotted fields - Joint seminar with Theoretical Physics

Mathematical Physics Seminar

13th October 2017, 2:00 pm – 3:00 pm
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 $f:\mathbb{R}^3\to\mathbb{C}$ 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.

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