Knots are a familiar part of everyday life, for example tying your tie or doing up your shoe laces. They play a role in numerous physical and biological phenomena, such as the untangling of DNA when it replicates.

However, knot theory is also a well-developed branch of pure mathematics.

In his talk, Marc gives an introduction to this theory and places it in the context of the modern field of topology. This is the branch of mathematics where you are allowed to stretch and deform objects, but not tear them. He explains how topological techniques can be used to prove some surprising facts about knots. He also gives some problems about knots that mathematicians haven't yet been able to solve.

Marc Lackenby is a Professor of Mathematics in Oxford and a Fellow of St Catherine's College.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.