Dear Christian, 



Please find below my Title and Abstract, for your conference. Note 
that I will stay from 16.05 until 24.05. You told me that you could 
support accomodation and probably the travel expenses. 
Tell me what 
holds.
 

Amitiés

Gérard



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Title : Algebras of diagrams and the EGF Hadamard Product

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%
Abstract
%%%%%%%

In this talk, we consider two aspects of the Hadamard product formula 
(HPF) for formal power series applied to combinatorial field theories.
Firstly, we remark that the case when the functions involved in the 
HPF have a constant term is of special interest as often these functions give rise to substitutional groups. The groups arising from the normal ordering problem of boson strings are naturally associated with explicit vector fields, or their conjugates, in the case when there is only one annihilation operator. These groups, which can be analytically expressed as groups of "Substitutions with prefunctions" are equivalent to classical notions like Riordan groups, classical Sheffer conditions and the « exponential formula ».
 Secondly, we discuss the Feynman-like graph representation resulting
 from the product formula. Natural deformations (counting graph 
parameters as crossings and superpositions) can be introduced in the 
product law to give a three parameter (two formal - or continuous - and one boolean) true Hopf deformation of this algebra of Feynman-like diagrams. We show that, for some values of the parameters, one recovers the algebra of Noncommutative Matrix Quasi-symmetric functions. Thus, we can see that one obtains, as a specialized homomorphic image, the algebra of Quasi-symmetric functions and then (with a restricted domain) the algebra of Euler-Zagier sums which, in turn, is related to the algebra of the Feynman Diagrams of perturbative Quantum Field Theory. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%