Knotty Problems - Marc Lackenby

Explore the fascinating world of knot theory in this Oxford Mathematics Public Lecture by Professor Marc Lackenby. Delve into the mathematical principles behind everyday knots and their significance in physical and biological phenomena. Learn about topology and its application to knot theory, discovering surprising facts and unsolved problems in this field. Gain insights into Tait's knot tabulation, crossing numbers, manifolds, Seifert surfaces, and the classification of surfaces with boundary. Examine the complexity of knots, including Wolfgang Haken's contributions, and understand how mathematicians approach the enumeration of knots. This 52-minute talk offers a comprehensive introduction to knot theory, bridging the gap between familiar knots and advanced mathematical concepts.

Intro
What is a knot?
Mathematics of knots
Tait's tabulation of knots
The crossing number of connected sums
Using topology - manifolds
Classification of surfaces with boundary
Building a Seifert surface
The genus of knot
The complexity of knots
Wolfang Haken and knots
The number of knots