University of California, San Diego.
Academic year: 2017-2018; Spring.
Monday 3:00-4:00.
APM 7218.

Date Speaker Topic
Jan 22 Jesse Levitt
  The Faithfulness of the Burau Representation and The Jones Unknot Conjecture


The Burau representation of the braid group was introduced in the 1930s and has been used since the 1980s to understand the Jones polynomial. A critical component of this study has been trying to understand when the Burau representation is faithful. It is known to be faithful for the Braid group on fewer than 4 strands and unfaithful on more than 4 strands. If the representation is unfaithful on 4 strands, it will solve the Jones unknot conjecture. We will review the current state of knowledge and some new approaches suggested by the work of Armond, Huynh and Le.