**
Claude Sabbah
**

**Hermitian metrics on some Frobenius
manifolds.
**

**Abstract
**

I will recall how a canonical Frobenius manifold structure can be
defined on the parameter space of the universal unfolding of any
(convenient and nondegenerate) Laurent polynomial. I will explain how
to construct a *tt ^{*}* structure on this parameter
space. The main theorem is the positive definiteness of the
corresponding Hermitian form. It is obtained through a description of
the Fourier-Laplace transform of a variation of polarized complex
Hodge structure defined on the complex line minus a finite set of
points.