Seminar - Janis Lazovskis

A Gentle Introduction to Knots and Knot Invariants

Abstract:

How many ways can you embed a circle in 3-space? This question motivates most of knot theory, and the first part of this presentation. Following a primer on the basics of knots, I will introduce some widely used knot invariants, from the Alexander and the Kauffman, to the Vasilievs and the Khovanov. Of the stronger ones, Vasiliev's invariants have a very combinatorial flavor, through the use of chord diagrams, while Khovanov's has a distinctly homological structure. Finally, if time permits, I will describe braid groups and the power that comes with this formalized approach. A reception at the Graduate House will follow the talk.