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Titlebook: Real and Complex Singularities; São Carlos Workshop Jean-Paul Brasselet,Maria Aparecida Soares Ruas Conference proceedings 2007 Birkhäuser

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Valuations Compatible with a Projection,e study the valuations on the ring . that extend .. All these valuations are described when . is a monomial valuation whose weight vector is not orthogonal to any of the faces of the Newton Polyhedron of the discriminant of the projection .. This description is done in terms of the Puiseux parameterizations of . with exponents in a cone.
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,Vertices and Inflexions of Plane Sections of Surfaces in ℝ3,of smooth surfaces by families of planes parallel to the tangent plane at a given point. We cover all the generic cases, namely elliptic, umbilic, hyperbolic, parabolic and cusp of Gauss points. This work is preliminary to an investigation of symmetry sets and medial axes for these families of curves, reported elsewhere.
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Local Topology of Reducible Divisors,2)-connected provided that the divisor has normal crossings outside of the singularity of .. We apply this result to obtain a vanishing property for the cohomology of local systems of rank one and also study vanishing in the case of local systems of higher rank.
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The Geometry of Flecnodal Pairs,immersed in ℝ. is studied in more detail, with the generic singularities of the flecnodal normals and the flecnodal tangents classified. Finally, the connection between the flecnodals and bitangencies are studied, especially in the case where the dimension of the manifold equals the codimension.
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,Path Formulation for ,, ⊕ ,,-equivariant Bifurcation Problems,on we observe the presence of only one modal parameter in the generic core. It differs from the classical classification where the core has 2 modal parameters. We finish this work comparing our classification to the one obtained in [.].
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