The Mathematics of Knots

This is an ACEMS Virtual Public Lecture featuring Professor Jessica Purcell from the School of Mathematics at Monash University

Abstract:
We encounter knots in everyday life - for example in phone chargers and shoelaces. A mathematical knot is obtained by fusing together the ends of a phone charger or shoelace. Mathematicians who study knot theory try to classify different ways of knotting: When can that shoelace be unknotted, or moved through space to have no crossings, without cutting it? Knots first appeared in mathematical literature in the 1700s, but knot theory really caught on in the late 1800s, when potential applications arose in physics.
In modern times, knots appear in protein folding, in strands of DNA, in quantum entanglement, as well as in the usual phone chargers and shoelaces. In this lecture, Professor Purcell provides an introduction to knot theory looking closely at some of the modern tools used to study them.

Moderator: ACEMS Deputy Director Tim Garoni, Monash University