Livestream: https://youtube.com/live/WyF42OPyeKQ

This talk is a biased introduction to knot theory and low-dimensional topology, and an overview of the rest of the series. We will start by introducing knotted curves in 3-space and knotted surfaces in 4-space, and discuss how one can represent and (partly) visualize them. We will then discuss different notions of equivalence for knots and surfaces, and assert some theorems and examples related to the existence and uniqueness questions for surfaces. Time permitting, we will introduce the Jones polynomial, an important but still somewhat mysterious tool from the 1980s for studying knots. We will end by overviewing the rest of the series and mentioning some of the most famous (and active) open problems in the area.

Most of this talk should be accessible to undergraduate students who have taken a course that introduces metric spaces.

Minerva Course Materials