Knots: from reality to mathematics and back

This lecture by Prof. John Maddocks from EPFL explores the journey of knots from practical applications to mathematical theory and vice versa. Starting with the equilibrium of ropes and hitches, the lecture delves into force balance conditions, tension analysis, and capstan inequalities on cylindrical surfaces. The presentation also covers the ideal shapes of knots, the mechanics of DNA knots, and the comparison between mathematically ideal and real-world trefoil knots. The discussion extends to orthogonal clasps, contact regions, and pressure distributions, highlighting the discrepancies between classic capstan analysis and finite tube radius scenarios. The lecture concludes with insights on the challenges and opportunities in understanding interacting tubes and interwound structures, emphasizing the relevance of accurate X-ray tomography data.