2011 An Introduction to Physical Knot Theory
Course contents (6 hours):
- Topological dynamics of physical knots
- Vortex knots, links and tangles
- Helmholtz equation, conservation laws, Biot-Savart law and LIA
- Torus knot solutions, vortex links.
- Vortex tangles, energy-complexity relations.
- Magnetic knots and braids
- Lorentz force, inflexional state and Reidemeister type I move, curly knots and braids.
- Magnetic relaxation, topological bounds on energy.
- Groundstate energy of tight knots, energy spectrum.