Semester:
Offered:
Peter B. Kronheimer (Department of Mathematics)
First-Year Seminar 52K credits (fall term) Enrollment: Limited to 12
Prerequisites: No background in mathematics is expected or required, and enrollees who are not intending to concentrate in mathematics will be particularly welcome.
Beyond their practical use in fastening ropes, knots have appeared frequently in the decorative arts and (somewhat less frequently) in the physical and life sciences. This first-year seminar will explore the world of knots in all its aspects, but our focus will be on a non-technical introduction to knots from the viewpoint of the mathematician, for whom knot theory is an active and ever-expanding field of research.
The basic mathematical questions about knots center around classification. What does it mean to classify knots? How can we understand that an overhand knot and a figure-eight knot are really different?
Alongside these questions, we will touch on other topics in the mathematical sciences that have connections to particular scientists and mathematicians who have made important contributions to knot theory. In particular, we will be motivated by the work of Peter Guthrie Tait, Max Dehn, and Joan Birman, and through their work we will be led to examine colorings of maps, dissections of polyhedra, and the knots that arise from the chaotic dynamics of the atmosphere.