Title: Honors Thesis: On the faithfulness of the Burau representation at roots of unity,
Abstract: We study the kernel of the evaluated Burau representation through the braid
element $\sigma_i \sigma_{i+1} \sigma_i$. The element is significant as a part
of the standard braid relation. We establish the form of this element's image
raised to the $n^{th}$ power. Interestingly, the cyclotomic polynomials arise
and can be used to define the expression. The main result of this paper is that
the Burau representation of the braid group of $n$ strands for $n \geq 3$ is
unfaithful at any primitive root of unity, excepting the first three.