Math Colloquium talk - "From Linking of Letters in Words to Invariants of Links"

Abstract:
In the topological theory of knots and links, we learn about Gauss' linking number - an integer measuring whether two circles in space are inextricably linked together. In this talk, I will explain that the same idea works for occurrences of letters in words. Here, a "word" is a way to represent a product of elements in a group, such as 'xyxxzy', and linking of its letters helps determine whether the corresponding product is inextricably different from 1. Closing a knotted loop, we'll discuss how this new approach to studying words sheds light on the very theory that inspired it: in ongoing joint work, we're discovering ways to tell apart links in 3D that were previously thought to be impossible.
The talk is meant to be accessible and will not require any background.