The fifth in our 2005 lecture series
Figuring Minds

SATURDAY, November 5 at 5:00pm
WHERE THE WILD THINGS ARE
A Talk about Knot Theory
by Ken Millett [IFF-L11]

at The Foshay Masonic Lodge
9635 Venice Blvd
Culver City
[Two blocks West of the Museum of Jurassic Technology and CLUI]

In mathematical lore, a topologist is a person who can’t tell the difference between a coffee cup and a donut, both objects being topologically the same. Of the many things topologists strive to categorize, one of the more enigmatic is knots. Though knotting is one of humanity’s oldest and most widespread activities, being documented in almost every culture on earth, at first glance it seems an unlikely subject for the formalisms of mathematics. But at the end of the nineteenth century mathematicians began to classify these twisted and braided forms, leading to a vast taxonomy of the species, whose members include the unknot, ideal knots, tame knots and wild knots.

Today, the insights of knot theory are being bought to bear on problems in biology and chemistry, specifically to understanding the structure of DNA and other macromolecules such proteins and polymers, and to fundamental issues in theoretical physics, where “string theory” proposes that all matter is composed of knot-like contortions in spacetime. In this lecture, Dr. Ken Millett, a leading knot theorist and professor of mathematics at the University of California, Santa Barbara, will discuss the history, theory, and taxonomy of knots. The event will include hands-on activities making knots and attempting to answer such questions as how much rope is required to make a specific knot, and how we determine if two seemingly disparate knots might really be the same.

After the lecture please join us for a reception at the Museum of Jurassic Technology, two blocks away. The Museum has recently opened its wonderful new exhibition on string figures.
As an undergraduate at MIT, Ken Millett was first drawn to engineering, then to physics, and ultimately to mathematics, specifically to geometry and topology, because, he says “these have served as the language of expression and means to study the mysteries of the natural sciences.” In the 1980’s Millett was involved in the discovery of several classes of “knot invariants,” polynomial equations that help mathematicians to categorize knots, and he participated in the development of topological quantum field theory. He is currently working on applying knot invariants to questions arising in molecular biology, including the structure of DNA. At the other end of the scale, models arising from these methods also apply to solar storms. Dr Millett is an authority on polygonal modeling of knots and is a leading researcher investigating the spatial characteristics of knotted materials.
"Ideal Knot" (top): courtesy of Ken Millett and Jason Cantarella
Knot images (above): courtesy of Eric Rawdon and Michael Piatek
(created using KnotPlot, a program for visualizing and exploring knots by Rob Scharein)