Applying the Temperley-Lieb Algebra to the 4-Colour Theorem

Sabin Cautis

Harvard University

April 7,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

The Temperley-Lieb algebra $TL_n(q)$ is a deformation of the symmetric group algebra coming from statistical mechanics. Some of its neat properties may be seen by relating it to the meander problem (counting non-intersecting closed planar paths through $2n$ fixed points on the line).

We will motivate a generalization $TL_n(x,y)$ of $TL_n(q)$ via an attempt to understand the Birkhoff-Lewis equations (which some hope may be used to give an algebraic proof of the four-colour theorem). $TL_n(x,y)$ is related to generalized Chebyshev polynomials and in a way is the greatest generalization we can make without losing many of the nice properties of $TL_n(q)$.

This talk is accessible to a general audience and presents joint work with David Jackson.


Speaker's Contact Info: scautis(at-sign)math.harvard.edu


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