This book contains papers growing out of recent work of the Singularity Seminar at Moscow State University. The main topic of most of the papers is the analysis of singularities of discriminant hypersurfaces formed by the degenerate objects in different spaces of mappings. Among the topics covered are: the space of mappings of the circle to three-space; invariants, bifurcations, and classifications of plane curves; algebraic invariants of the Morse complex; complex boundary singularities; spaces of morsifications of singularities; and the number of singular points on a complex projective hypersurface.
Tree-like curves by F. Aicardi Plane curves, their invariants, perestroikas and classifications by V. I. Arnold The framed Morse complex and its invariants by S. A. Barannikov Vassiliev knot invariants I. Introduction by S. V. Chmutov, S. V. Duzhin, and S. K. Lando Vassiliev knot invariants II. Intersection graph conjecture for trees by S. V. Chmutov, S. V. Duzhin, and S. K. Lando Vassiliev knot invariants III. Forest algebra and weighted graphs by S. V. Chmutov, S. V. Duzhin, and S. K. Lando Symmetric quartics with many nodes by V. V. Goryunov Subprincipal Springer cones and morsifications of Laurent polynomials and $D \mu$ singularities by V. V. Goryunov On the enumeration of curves from infinity to infinity by S. M. Gusein-Zade On the classification of ornaments by A. B. Merkov Boundary singularities: Topology and duality by I. Shcherbak and A. Szpirglas Invariants of ornaments by V. A. Vassiliev.