The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

CSM

Seminar

Complex zeros of the chromatic and Tutte polynomials

Sokal, A (New York)
Monday 21 January 2008, 10:00-11:00

Seminar Room 1, Newton Institute

Abstract

In this introductory talk, I begin by showing how the chromatic and flow polynomials are special cases of the multivariate Tutte polynomial, and I sketch why it is often advantageous to "think multivariate", even when one is ultimately interested in a univariate specialization. I then explain briefly why the complex zeros of these polynomials are of interest to statistical physicists in connection with the Lee-Yang picture of phase transitions. Finally, I summarize what is known -- and above all, what is _not_ known -- about the complex zeros of these polynomials.

A general reference for this talk is:

arXiv:math/0503607 [math.CO] Alan D. Sokal The multivariate Tutte polynomial (alias Potts model) for graphs and matroids

More details on various aspects can be found in:

arXiv:math/0301199 [math.CO] Gordon Royle, Alan D. Sokal The Brown-Colbourn conjecture on zeros of reliability polynomials is false

arXiv:math/0202034 [math.CO] Young-Bin Choe, James G. Oxley, Alan D. Sokal, David G. Wagner Homogeneous multivariate polynomials with the half-plane property

arXiv:cond-mat/0012369 [cond-mat.stat-mech] Alan D. Sokal Chromatic roots are dense in the whole complex plane

arXiv:cond-mat/9904146 [cond-mat.stat-mech] Alan D. Sokal Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions

Audio

MP3MP3

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧