Abstract of M Baechtold's talk

The subject of my talk are "geometric" generalized solutions of
nonlinear PDEs and the singularities which these solutions exhibit. I
will start by reviewing the geometric approach to nonlinear PDEs and
the concept of diffiety to which this leads. I then introduce the
aforementioned generalized solutions and explain how to a PDE E one
may associate new PDEs whose solutions describe the "shape" of
singularities of solutions to E. The remaining time will be dedicated
to singularities of fold-type and their relation to the characteristic
variety of a nonlinear PDE.