Abstract:Differentiable mappings of smooth manifolds possess singularities. The cohomology class Poincare dual to the locus of particular singularity type is expressed as a universal polynomial (known as the Thom polynomial) in the characteristic classes of manifolds participating in the mapping. The very existence of such polynomial provides also a way of its explicit computation. This leads to an efficient solution of many enumerative problems of complex projective enumerative geometry. We will discuss details of this approach to enumerative geometry as well as some variations of the Thom polynomial theory including enumeration of isolated hypersurface singularities, singularities of wave fronts, and multisingularities of various kinds.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006