Subjects of investigations
Differential equations in the complex domain.
Links between integrability and existence of geometric transversal structures.
Conformal pseudo-groups in complex dimension 1.
Systematical study of subgroups of Diff(C,0).
Existence of invariant geometrical structure
(generalisations of Lie Theorem on geometries of the line).
Singularities of holomorphic foliations.
Systematical study of cuspidal singularities
(topological, formal, analytic and dynamic).
Transversal structure of any singularity in dimension 2
(generators of the pseudo-group).
Problem of normal forms and existence of versal family
(codimension 1 foliations and planar vector fields).
Singular foliations on compact complex manifolds.
Construction of chaotic foliations by curves on projective spaces.
Study of codimension 1 foliations on compact manifolds.