New developments in singularity theory : proceedings of the NATO Advanced Study Institute, Cambridge, UK, 31 July - 11 August 2000

singularities Arise Naturally In A Huge Number Of Different Areas Of Mathematics And Science. As A Consequence, Singularity Theory Lies At The Crossroads Of Paths That Connect Many Of The Most Important Areas Of Applications Of Mathematics With Some Of Its Most Abstract Regions. The Main Goal In Most Problems Of Singularity Theory Is To Understand The Dependence Of Some Objects Of Analysis, Geometry, Physics, Or Other Science (functions, Varieties, Mappings, Vector Or Tensor Fields, Differential Equations, Models, Etc.) On Parameters. The Articles Collected Here Can Be Grouped Under Three Headings. (a) Singularities Of Real Maps; (b) Singular Complex Variables; And (c) Singularities Of Homomorphic Maps. Front Matter....Pages i-viii Front Matter....Pages 1-1 Classifications in Singularity Theory and Their Applications....Pages 3-33 Applications of Flag Contact Singularities....Pages 35-64 On Stokes Sets....Pages 65-86 Resolutions of discriminants and topology of their complements....Pages 87-115 Classifying Spaces of Singularities and Thom Polynomials....Pages 117-134 Singularities and Noncommutative Geometry....Pages 135-155 Front Matter....Pages 157-157 The Geometry of Families of Singular Curves....Pages 159-192 On the preparation theorem for subanalytic functions....Pages 193-215 Computing Hodge-theoretic invariants of singularities....Pages 217-233 Frobenius manifolds and variance of the spectral numbers....Pages 235-255 Monodromy and Hodge Theory of Regular Functions....Pages 257-278 Bifurcations and topology of meromorphic germs....Pages 279-304 Unitary reflection groups and automorphisms of simple hypersurface singularities....Pages 305-328 Simple Singularities and Complex Reflections....Pages 329-348 Front Matter....Pages 349-349 Discriminants, vector fields and singular hypersurfaces....Pages 351-377 The theory of integral closure of ideals and modules: Applications and new developments....Pages 379-404 Nonlinear Sections of Nonisolated Complete Intersections....Pages 405-445 The Vanishing Topology of Non Isolated Singularities....Pages 447-472