Our different goals and scientific interests are interlinked and form a nucleus around the geometric study singularities of varieties, dynamical systems and differential equations. It is divided into the following sections (the usual techniques in brackets):

1. Reduction of singularities and applications (Algebraic and Analytic Geometry Complex).
2. Existence and explicit construction of solutions of differential equations ordinary and partial differential (Newton polygon and polyhedron).
3. Asymptotic expansion in several variables and functions of Gevrey type. Nature of solutions (summability, asymptotic analysis and functional).
4. Galois theory of differential equations (differential algebra).
5. Geometric study of singularities of vector fields (differential equations, real analytic geometry).
6. Topological classification of vector fields in dimension three. (Hartman-Grobman, explosions)
7. Singular Holomorphic Foliations, local and global study. (Complex geometry, reduction of singularities, holonomy).
8. Dynamics associated with holomorphic diffeomorphisms in several variables. (Summability, resurgence, normal forms).