WoG 2024 Talk 2.3: Donsung Lee - On the Faithfulness of the Burau Representation of $B_3$ Modulo $p$

Speaker: Donsung Lee
Institution: Seoul National University
Title: On the Faithfulness of the Burau Representation of $B_3$ Modulo $p$
Abstract: The Burau representation is one of the most extensively studied representations of the braid group. While the question of its faithfulness has a long history, the case of $B_3$ was relatively easily solved in the mid-20th century by using the fact that the quotient of $B_3$ by its center is isomorphic to the modular group. In this talk, I try to extend this result to the Burau representation of $B_3$ modulo $p$, where $p$ is any prime, and I present an algorithm for determining whether the representation is faithful, given a prime $p$.