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

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

  Abstract:

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.