Dipartimento di Matematica "Guido Castelnuovo"

Universita' degli Studi di Roma "la Sapienza"

Piazzale Aldo Moro, 2

00185 - Roma, ITALY

E-mail: fiorenza@mat.uniroma1.it

**Associative algebras, punctured disks and the quantization
of Poisson manifolds**

**Abstract:**

The aim of the talk is to provide an introduction to the algebraic,
geometric and quantum field theoretic ideas that lie behind the Kontsevich-Cattaneo-Felder
formula for the quantization of Poisson structures, and to show how the
quantization formula itself naturally arises when one couples the form
a Feynman integral should have in order to reproduce the given Poisson
structure as the first order term of its perturbative expansion with the
form it should have to describe an associative algebra. It is further shown
how the Koszul-Magri brackets on 1-forms naturally fits into the theory
of the Poisson sigma-model.

This is a joint work with Riccardo Longoni.