The Complexity of Knots - A Computational Approach

Explore a mathematical lecture from Harvard CMSA where Marc Lackenby from the University of Oxford delves into the computational complexity of knot theory, beginning with Alan Turing's 1954 observation about the lack of systematic methods for determining knot equivalence. Learn about the subsequent developments by Wolfgang Haken and Geoffrey Hemion, who discovered methods for comparing knots, while examining the ongoing challenges in determining the computational complexity of these problems. Discover recent advances in the field, particularly focusing on a theorem that establishes polynomial bounds for the number of Reidemeister moves needed to transform between different diagrams of the same knot type, suggesting that knot problems may be more computationally manageable than previously thought.