Classes caractéristiques et théorèmes d'indice : point de vue microlocal
Lieu des pôles d'un système holonome d'équations aux différences finies
Équations différentielles à points singuliers irréguliers en dimension 2
Harmonic metrics and connections with irregular singularities
We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface with the complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same complex.
Non-commutative Hodge structures
This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.
Moduli of pre-...-modules, preverse sheaves and the Riemann-Hilbert morphism. I.
Equations aux différences finies et déterminants d'intégrales de fonctions multiformes.
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.
Hypergeometric periods for a tame polynomial.
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