UC Berkeley

This dissertation concerns two subjects that the author explored in his doctoral research: the Burau representation of the braid groups and moduli spaces of Euclidean cone surfaces. We present some general theory on each subject and the connection that eventually ties the two together. In particular, we see original results of the author that leverage the geometry of the moduli spaces of flat cone spheres to identify the kernel of certain evaluations of the Burau representation at roots of unity. Figures abound.