*Physical Applications of Knot Theory* (Torino, 2005-2008)

Course contents (20 hours):

- Introduction to space curves and knot theory
- Fundamentals of space curves
- Global geometric aspects of space curves
- Knots, links and projections
- Gauss linking number
- Calugareanu-White invariant
- Measures of structural complexity
- Articles included:
- By Ricca, R.L. (2005) on
*Knot Theory. Structural complexity.*
- By Hoste, J., Thistlethwaite M. & Weeks, J. (1998) on
*The first 1,701,936 knots*

- Topological equivalence classes and change of topology
- Topological equivalence classes for frozen fields
- Change of topology
- Measuring structural complexity: a test case
- Articles included:
- By Ricca, R.L. & Berger, M.A. (1996) on
*Topological ideas and fluid mechanics*
- By Ricca, R.L. (1998) on
*Applications of knot theory in fluid mechanics*

- Vortex dynamics, knots and links
- Elements of vortex dynamics
- Vortex knots and links
- Conservation laws and topology
- Articles included:
- By Moffatt, H.K. (1969) on
*The degree of knottedness of tangled vortex lines*
- By Arnold, V.I. (1974)
*The asymptotic Hopf invariant and its application*

- Ideal magnetohydrodynamics of knotted and braided flux-tubes
- Ideal magnetohydrodynamics and analogous Euler's flows
- Lorentz force and inflexional disequilibrium of flux-tubes
- Magnetic relaxation under topological constraints
- Articles included:
- By Moffatt, H.K. & Ricca, R.L. (1992) on
*Helicity and the Calugareanu invariant*
- By Freedman, M.H. (1988)
*A note on topology and magnetic energy in incompressible perfectly conducting fluids*

- Magneto-elastic relaxation of braids and strings
- Topological bounds on magnetic braids.
- Elastic relaxation and supercoiled strings.
- Elastic energy and knot type.
- Articles included:
- By Berger (1993) on
*Energy-crossing number relations for braided magnetic fields*
- By Katritch et al. (1996) on
*Geometry and physics of knots*
- By Sumners (1995) on
*Lifting the curtain: using topology to probe the hidden action of enzymes*