Temperley and Lieb presented a transfer‐matrix approach to study problems related to the study

of percolation and coloring problems on an infinite 2‐dimensional lattice. They noted that the

transfer matrices respected a certain list of relations, which led to the introduction and study of the

so‐called Temperley‐‐Lieb algebras. Temperley‐‐Lieb algebras are intimately related to knot theory.

The Jones polynomial of a knot can be derived from a representation of the braid group into the

Temperley‐Lieb algebra, the so‐called Burau representation. The "Jones unknotting conjecture"

states that Jones polynomials distinguish the unknot from nontrivial knots. In this talk, we will

introduce Jones polynomials through Temperley‐Lieb algebras and describe a current program that

aims to find a nontrivial knot with a trivial Jones polynomial through Burau's unfaithful

representation.

### Time & Location

Jun 12, 2020 | 10:00 AM

WebEx

Please ask a member of the work group for further information (e.g. Jonathan Kliem).