Galois theory of fuchsian q-difference equations
Gauge-equivalent deformations of linear ordinary differential operators with constant coefficients.
Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)
We associate to any convenient nondegenerate Laurent polynomial on the complex torus a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of (or its universal unfolding) and of the corresponding Hodge theory.
Geometry and analytic theory of Frobenius manifolds.