This text offers a selection of papers on singularity theory presented at the Sixth Workshop on Real and Complex Singularities held at ICMC-USP, Brazil. It should help students and specialists to understand results that illustrate the connections between singularity theory and related fields. The authors discuss irreducible plane curve singularities, openness and multitransversality, the distribution Afs and the real asymptotic spectrum, deformations of boundary singularities and non-crystallographic coxeter groups, transversal Whitney topology and singularities of Haefliger foliations, the topology of hypersurface singularities, polar multiplicities and equisingularity of map germs from C3 to C4, and topological invariants of stable maps from a surface to the plane from a global viewpoint.
Irreducible plane curve singularities, Abramo Hefez; openness and multitransversality, C.T.C. wall; the distribution A and the real asymptotic spectrum, Daniel Barlet and Ahmed Jeddi; deformations of boundary singularities and non-crystallographic Coxeter Groups, Ina Scherbak; transversal Whitney topology and singularities of Haefliger Foliations, Shyuchi Izumiya and Kunihide Maruyama; on a Conjecture of Chisini for coverings of the Plane with A-D-E-singularities, Valentine S. Kulikov; not all codimension 1 germs have good real pictures, David Mond and Roberta G. Wik Atique; on the topology of hypersurface singularities, Jose Seade; polar multiplicities and equisingularity of map germs from C3 to C4, Victor Hugo Jorge Perez; topological invariants of stable maps from a surface to the plane from a global viewpoint, D. Hacon, C. Mendez de Jesus, and M.C. Romero Fuster; cubics in R and C, Radmila Bulajich, Leon Kushner, and Santiago Lopez de Medrano; indices of Newton non-degenerate vector fields and a conjecture of Loewner for surfaces in R4, Carlo Gutierrez and Maria Aparecida Soares Ruas; generic singularities of H-directions, Luis Fernando O. Mello; vertices of curves on constant curvature manifolds, Claudia C. Pasonato and Sueli I.R. Costa; projections of hypersurfaces in R4 to planes, Ana Claudia Nabarro; Frobenius manifolds and hypersurface singularities, Claus Hertling.