(10h30 pour le café, salle Fokko du Cloux - 1er étage - Bât. Doyen Jean Braconnier - 
Université Claude Bernard Lyon1 - La Doua) 
Tuesday, April 24, 10:45

Title: Beraha numbers, Tutte polynomial and its topological generalization.

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 noninteger Beraha number can never be a root of the  
chromatic polynomial of any graph. Nevertheless, it seems that the roots of the
chromatic polynomial of a planar triangulation tend to accumulate around the 
Beraha numbers. In the talk I first briefly review the Beraha numbers and then 
turn to the Tutte polynomial which specializes to the chromatic polynomial. 
I plan also discuss applications of the Tutte polynomial in knot theory and 
its generalizations motivated by topology. In particular, I would like to 
present a recently introduced Tutte-Krushkal-Renardy polynomial for cell 
complexes which may be regarded as a higher dimensional version of the Tutte 
polynomial.