The R. Kent Nagle Lecture Series
February 16, 2006
Louis H. Kauffman explores the topic “Unknots, Collapsing Tangles,
and DNA Recombination”
Date: February 16, 2006
Time: Thursday evening 7:30-8:30 p.m.
Place: BSF 100, at USF-Tampa, located in front of the Physics Building
Parking: There is free parking available in the Lots 2A and 2B, adjacent
to the lecture hall. Additional free parking will be available in Lot 1
(adjacent to the Administration Building) if necessary.
Louis H. Kauffman
Louis H. Kauffman
Unknots, Collapsing Tangles, and DNA Recombination
A description of the talk:
Magicians often present their audience with a knotted rope that miraculously
unties itself. The secret to this trick is not always in a sleight-of-hand, but
rather in topology! One can make “knots” that look knotted but are
really not knotted. How can we recognize if a knot is really knotted? This is
the fundamental question in knot theory. In this talk we begin with a discussion
of the basics of knot theory and some very intriguing questions about the
complexity of diagrams for unknots. We follow this path and find ourselves in
the subject of rational tangles (certain weaving patterns that correspond to
rational numbers) and some elementary number theory. Returning, we find that we
have constructed infinitely many unknot diagrams that are hard to untie in the
sense that they have to be made more complicated before they simplify. We find
the smallest such unknot and we apply these ideas to DNA. The DNA molecule can
start in an unknotted state and get knotted by the repeated application
recombination enzymes. The theory of tangles and knots applies to unlocking the
mechanisms of DNA recombination. This work is done in collaboration with Sofia
Lambropoulou of NTUA, Athens, Greece.
A description of the speaker:
Louis H. Kauffman is a professor of Mathematics at University of Illinois at
Chicago. He received his Ph.D. from Princeton, and has worked at many places as
a visiting professor and researcher, including the University of Zaragoza in
Spain, the University of Iowa in Iowa City, the Institute Hautes Etudes
Scientifiques in Bures Sur Yevette, France, the Institute Henri Poincaré
in Paris, France, the Universidad de Pernambuco in Recife, Brazil, and the
Newton Institute in Cambridge England. He is the founding editor and one of the
managing editors of the Journal of Knot Theory and its Ramifications, and
editor of the World Scientific Book Series On Knots and Everything. He is the
author of the books “Formal Knot Theory”, “On Knots”,
“Temperley Lieb Recoupling Theory”, and “Invariants of
3-Manifolds” (Princeton University Press), and “Knots and
Physics” (World Scientific Pub. Co.). He has been a prominent leader in
Knot Theory, one of the most active research areas in mathematics today. His
discoveries include a state sum model for the Alexander-Conway Polynomial, the
bracket state sum model for the Jones polynomial, the Kauffman polynomial, and
Virtual Knot Theory. Many important concepts in the field bear his name. His
publication list numbers over 170 and continues to grow, and with intriguing
new results and concepts. He continues to inspire young mathematicians in the
field.