Unknotting knots: Khovanov Homology and a less violent approach to the Gordian problem

Series: 
Research Horizons Seminar
Wednesday, September 15, 2010 - 12:00
1 hour (actually 50 minutes)
Location: 
Siles 171
,  
School of Mathematics - Georgia Institute of Technology

Hosted by Yao Li and Ricardo Restrepo.

 Deciding how to unknot a knotted piece of string (with its ends glued together) is not only a difficult problem in the real world, it is also a difficult and long studied problem in mathematics. (There are several notions of what one might mean by "unknotting" and I will leave the exact meaning a bit vague in this abstract.) In the past mathematicians have used a vast array of techniques --- from geometry to algebra, and even PDEs --- to study this question. I will discuss this question and (partially) recast it in terms of 4 dimensional topology. This new perspective will allow us to use a powerful new knot invariant called Khovanov Homology to study the problem. I will give an overview of Khovanov Homology and indicate how to study our unknotting question using it.