event 17 October 201119:30

Venue: Trinity College Dublin
Date: Monday 17 October 2011
Time: 7.30pm
 

Quantum Theory of Knots

Abstract:

Geometry in the three dimensions of physical space and the four dimensions of spacetime has many unique features - many of them linked to Hamilton's quaternions. One facet of this is the development in the last century of a rich mathematical theory of knots.

Knot theory is unusual in that some of the deepest modern insights in this subject can be explained in down-to-earth terms that everyone can understand. I will show this in the case of the Jones polynomial, a wonderful insight about knots that was discovered nearly thirty years ago.

As a physicist, what interests me most about knots is that in a sense they are quantum mechanical in nature - many of the deepest insights about knots are most naturally understood using physics-based ideas of quantum theory. I will explain a physicist's view of the Jones polynomial and its contemporary cousin, Khovanov homology.

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