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Knots in light and fluids

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Topological Dynamics in the Physical and Biological Sciences

To tie a shoelace into a knot is a relatively simple affair. Tying a knot in a field is a different story, because the whole of space must be filled in a way that matches the knot being tied at the core. The possibility of such localized knottedness in a space-filling field has fascinated physicists and mathematicians ever since Kelvins ‘vortex atom’ hypothesis, in which the atoms of the periodic table were hypothesized to correspond to closed vortex loops of different knot types. An intriguing physical manifestation of the interplay between knots and fields is the possibility of having knotted dynamical excitations. I will discuss some remarkably intricate and stable topological structures that can exist in light fields whose evolution is governed entirely by the geometric structure of the field. A special solution based on a structure known as a Robinson Congruence that was re-discovered in different contexts will serve as a basis for the discussion. I will th en turn to hydrodynamics and discuss topologically non-trivial vortex configurations in fluids.

This talk is part of the Isaac Newton Institute Seminar Series series.

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