Singularity Theory and its Applications

James Montaldi is a Reader in Mathematics at the University of Manchester.

Symmetric lagrangian singularities and Gauss maps of theta divisors.- On infinitesimal deformations of minimally elliptic singularities.- C-Régularité et trivialité topologique.- Folding maps and focal sets.- The dual graph for space curves.- On the components and discriminant of the versal base space of cyclic quotient singularities.- - equivalence and the equivalence of sections of images and discriminants.- Differential forms and hypersurface singularities.- Local reflexional and rotational symmetry in the plane.- The intersection form of a plane isolated line singularity.- On the degree of an equivariant map.- Automorphisms of direct products of algebroid spaces.- Disentanglements.- The euler characteristic of the disentanglement of the image of a corank 1 map germ.- Vanishing cycles for analytic maps.- On complete conditions in enumerative geometry.- Right-symmetry of mappings.- Deformations and the milnor number of non-isolated plane curve singularities.- Vanishing cycles and special fibres.- On the versal deformation of cyclic quotient singularities.- On Canny's roadmap algorithm: orienteering in semialgebraic sets (an application of singularity theory to theoretical robotics).- Elliptic complete intersection singularities.- Pencils of cubic curves and rational elliptic surfaces.