School of Mathematical Sciences
Monday, March 21, 2011
Schreiber 006, 12:15
Moscow Steklov Institute and Independent University
Universal polynomials and enumerative geometry
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