Claude Sabbah

Hermitian metrics on some Frobenius manifolds.


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.