  In this work, we begin to uncover the architecture of the general family of
zeta functions and multiple zeta values as they appear in the theory of
integrable systems and conformal field theory. One of the key steps in this
process is to recognize the roles that zeta functions play in various arenas
using transform methods. Other logical connections are provided by the the
appearance of the Drinfeld associator, Hopf algebras, and techniques of
conformal field theory and braid groups. These recurring themes are subtly
linked in a vast scheme of a logically woven tapestry.
  An immediate application of this framework is to provide an answer to a
question of Kontsevich regarding the appearance of Drinfeld type integrals and
in particular, multiple zeta values in: a) Drinfeld's work on the KZ equation
and the associator; b) Etingof-Kazhdan's quantization of Poisson-Lie algebras;
c) Tamarkin's proof of formality theorems; d) Kontsevich's quantization of
Poisson manifolds. Combinatorial arguments relating Feynman diagrams to Selberg
integrals, multiple zeta values, and finally Poisson manifolds provide an
additional step in this framework. Along the way, we provide additional insight
into the various papers and theorems mentioned above. This paper represents an
overall introduction to work currently in progress. More details to follow. See
our paper Math.QA/[ ] for a proof of the Connes Kreimer Conjecture.
