The Shape of Knots: From DNA to Shoestrings and Solar Flares

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Knots are ubiquitous in the world around us, appearing as tangled cords, shoelaces, or the complex structures of DNA. Far from being nuisances, knots have profound and beautiful mathematical properties with tentacular connections to geometry, topology, physics, and biology. This lecture introduces the fascinating world of knot theory, exploring how the mathematical study of knots helps us understand and predict their formation, stability, and behaviour.

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Colin C. Adams. The Knot Book: An Elementary Introduction to the Mathematical Theory
of Knots. American Mathematical Society, Providence, RI, 2004.

Moritz Epple. Topology, matter, and space, I: Topological notions in 19th-century natural
philosophy. Archive for history of exact sciences, 52(4):297–392, 1998.

Alain Goriely. Knotted umbilical cords. In Physical and Numerical Models in Knot Theory:
Including Applications To the Life Sciences, pages 109–126. World Scientific, 2005.

Louis H. Kauffman. Knots and Physics, volume 1. World Scientific, Singapore, 2001.

Marc Lackenby. A polynomial upper bound on reidemeister moves. Annals of Mathemat-
ics, pages 491–564, 2015.

Marc Lackenby. Unknot recognition in quasi-polynomial time, 2021. Announced in 2021;
algorithm with running time 2O((log n)3).

Marc Lackenby. A polynomial upper bound on reidemeister moves for each link type. arXiv
preprint arXiv:2602.09923, 2026.

Charles Livingston. Knot theory, volume 24. Cambridge University Press, 1993.

Alexei Sossinsky. Knots: Mathematics with a Twist. Harvard University Press, Cambridge,
MA, 2002.

Carl Sundberg and Morwen Thistlethwaite. The rate of growth of the number of prime
alternating links and tangles. Pacific journal of mathematics, 182(2):329–358, 1998.

Steven A Wasserman, Jan M Dungan, and Nicholas R Cozzarelli. Discovery of a predicted
DNA knot substantiates a model for site-specific recombination. Science, 229(4709):171–
174, 1985.

© Professors Alain Goriely 2025-26

This event was on Tue, 09 Jun 2026

Professor Alain Goriely

Professor Alain Goriely FRS

Gresham Professor of Geometry

Alain Goriely is a mathematician with broad interests in mathematical methods, mechanics, sciences, and engineering. He is well known for his contributions to dynamical systems...

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