Unraveling Knotted Fields

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 Kelvin’s 'vortex atom' hypothesis, in which the atoms of the periodic table were hypothesized to correspond to closed vortex loops of different knot types. Perhaps the most intriguing physical manifestation of the interplay between knots and fields is the existence of knotted dynamical excitations. I will discuss some remarkably intricate and stable topological structures that can exist in light fields whose hydrodynamic-like evolution is governed entirely by the geometric structure of the field. I will then turn to experimental hydrodynamics: how to make knotted vortex loop configurations in fluids and how they evolve once made.