##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## 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 L\^e.

Host: Dan Rogalski

### May 21, 2018

### 3:00 PM

### AP&M 7218

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