Braids, Knots, and Quantum Dots

Lord Kelvin proposed in 1867 that the atoms are the knotted tubes of ether. This theory proved to be wrong but the study of knots and their classification remained an important problem, in mathematics for the next 100 years and then in both mathematics and physics to this day. In this semilab we shall first learn about the topology of knots and links in three dimensions, the notion of knot invariants, the simplest polynomial invariants of knots. We then turn to the physics of knots, and learn about an intriguing connection between the knotted paths and the elementary particles.