Real and Complex Singularities: São Carlos Workshop 2004: Trends in Mathematics

Celestial Integration, Stringy Invariants, and Chern-Schwartz-MacPherson Classes.- Valuations Compatible with a Projection.- Quelques Résultats sur Certaines Fonctions à Lieu Singulier de Dimension 1.- Classification of Rational Unicuspidal Projective Curves whose Singularities Have one Puiseux Pair.- Bounding from below the Degree of an Algebraic One-dimensional Foliation Having a Prescribed Algebraic Solution.- Trajectory Singularities for a Class of Parallel Motions.- Vertices and Inflexions of Plane Sections of Surfaces in ?3.- Local Topology of Reducible Divisors.- The Geometry of Flecnodal Pairs.- Path Formulation for Z 2 ? Z 2-equivariant Bifurcation Problems.- The Multiplicity of Pairs of Modules and Hypersurface Singularities.- Lagrangian and Legendrian Singularities.- F-manifolds from Composed Functions.- On Equisingularity of Families of Maps (?n, 0) ? (? n+1, 0).- Projected Wallpaper Patterns.- Modular Lines for Singularities of the T-series.- Do Moduli of Goursat Distributions Appear on the Level of Nilpotent Approximations?.- Calculation of Mixed Hodge Structures, Gauss-Manin Connections and Picard-Fuchs Equations.- Whitney Equisingularity, Euler Obstruction and Invariants of Map Germs from ?n to ?3, n > 3.- Versality Properties of Projective Hypersurfaces.- Minimal Intransigent Hypersurfaces.- On the Link Space of a ?-Gorenstein Quasi-Homogeneous Surface Singularity.- Singularity Exchange at the Frontier of the Space.- Mackey Functors on Provarieties.

The São Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains papers presented at the eighth workshop, held at the IML, Marseille, July 19–23, 2004.
The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities. This is reflected by the contributions in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.

Collects new results in singularity theory and its applications, from those elements which draw heavily on commutative algebra to the various flavours of geometry and topology Summary of current main ideas in singularity theory, suggesting future research directions in the area Includes supplementary material: sn.pub/extras