An Introduction to the Mathematical Theory of Knots and Links
In this Master Class we will explore a mathematical theory of knots and links by playing with colored strings. This intuitive approach, and its resulting knots and links, will lead us to computable classical topology invariants and results, including how various knots and links differ from each other. Along the way, we’ll survey the history of the topological theory of knots and links from its beginnings to its present flourishing state and its rich interactions with other areas of math and theoretical physics.
Sylvain Edward Cappell is a topologist who has spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he is now the Silver Professor of Mathematics. He is a graduate of the Bronx High School of Science, where he won first place in the Westinghouse Science Talent Search for his work on “The Theory of Semi-cyclical Groups with Special Reference to Non-Aristotelian Logic.” He is best known for his “codimension one splitting theorem,” which is a standard tool in high-dimensional geometric topology, and a number of important results proven with his collaborator Julius Shaneson. Their work includes many results in knot theory and aspects of low-dimensional topology.