Title: Higher dimensional Tutte polynomial.

Abstract: The Tutte polynomial for graphs can be generalized to the higher 
dimensional cell complexes. This was done recently by V.Krushkal and D.Renardy. 
It turns out that their polynomial is a particular case of the Tutte polynomial 
of some representable matroids. Thus it gives a topological interpretation for 
the combinatorial matroidal notions. I explain the relationship of the 
Tutte-Krushkal-Renardy polynomial with the other known results. In particular, 
I will show that evaluation of this  polynomial at the origin gives the number 
of cellular spanning trees in a sense of A.Duval, C.Klivans and J.Martin. 
Moreover, a slight modification of the Krushkal-Renardy polynomial lead to the 
weighted cellular spanning trees and therefore can be calculated by the cellular 
matrix-tree theorem. In the case of cell decomposition of a sphere this modified 
polynomial also satisfies the duality relation of Krushkal-Renardy. Another 
specialization of the Tutte-Krushkal-Renardy polynomial is the Bott polynomials 
introduced by Raoul Bott in 1952. This is a joint work with C.Bajo and B.Burdick.