Royal Holloway University of London
Wednesday, November 7

Title: Beraha numbers and graph polynomials.

Abstract: The n-th Beraha number is defined as $B_n =2+2cos(2\pi/n)$. According
to W. Tutte the Beraha numbers are tightly related to chromatic polynomials of
graphs. It is known that a non-integer Beraha number can never be a root of the 
chromatic polynomial of any graph. Nevertheless, conjecturally the roots of the
chromatic polynomial tend to accumulate around the Beraha numbers.
In the talk I first briefly review the Beraha numbers and then I turn to the Tutte
polynomial which specializes to the chromatic polynomial. After that I plan to
discuss applications of the Tutte polynomial in knot theory motivated by topology.