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

Sabin Cautis

Harvard University

April 7,
refreshments at 3:45pm


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)

Return to seminar home page

Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

Page loaded on March 18, 2004 at 01:16 PM. Copyright © 1998-99, Sara C. Billey. All rights reserved.