The Jones polynomial via quantum group representations

Series
Geometry Topology Student Seminar
Time
Wednesday, April 8, 2020 - 2:00pm for 1 hour (actually 50 minutes)
Location
Online
Speaker
Tao Yu – Georgia Tech – tyu70@gatech.edu
Organizer
Hongyi Zhou

Continuing the theme of Hopf algebras, we will discuss a recipe by Reshetikhin and Turaev for link invariants using representations of quantum groups, which are non-commutative, non-cocommutative Hopf algebras. In the simplest case with the spin 1/2 representation of quantum sl2, we recover the Kauffman bracket and the Jones polynomial when combined with writhe. Time permitting, we will also talk about colored Jones polynomials and connections to 3-manifold invariants.