Generic geometry
Differential geometry of smooth and singularity subvarieties in Euclidean spaces. Global classification of stable applications, flows and foliations on surfaces and 3-manifolds. Complete invariants for second order geometry. Application to string theory.
Singularities and applied geometry
Conformal geometry: rational curves of Pythagorean hodograph in computer-aided design. Geometric applications to microwave circuit design. Design of Bézier surfaces with prefixed boundary properties.
Singularities
Classification and obtaining analytic and topological invariants of singularities of differentiable and complex analytic applications. Lojasiewicz exponents and non-degeneracy conditions on analytic applications. Study of semilocal invariants of Vassiliev type.
