Georgia Institute of Technology College of Sciences

An element of the braid group can be visualized as a collection of n strings that are braided (like a hair braid). Braid groups are ubiquitous in mathematics in science, as they record the motions of a number of points in the plane. These points can be autonomous vehicles, particles in a 2-dimensional medium, or roots of a polynomial. We will give an introduction to and a survey of braid groups, and discuss what is known about homomorphisms between braid groups.