Masahiko YOSHINAGA

Title: 
Tutte polynomials in geometry and combinatorics. 

Abstract: 
The Tutte polynomial is an invariant of a finite graph, which is a polynomial 
in two variables. Tutte polynomials have lots of specializations, e.g., chromatic 
polynomial, Jones polynomials of alternating links, partition functions of Ising models, 
the expectation of chromatic polynomials of random graphs, etc. 
Recently L. Moci invented "arithmetic Tutte polynomials" associated to a finite list 
of integer vectors (more generally, to a finite list of elements in a finitely generated 
abelian groups). Arithmetic Tutte polynomials also carry lots of informations on 
topology of toric arrangements and enumerative problems of zonotopes. 
In this talk, we first recall definitions of Tutte and arithmetic Tutte polynomials and survey 
the above results. Then we introduce G-Tutte polynomials which unify the above 
and other polynomial invariants. (The second half of this talk is based on 
a joint work with Ye Liu, Tan Nhat Tran.)