  We classify all possible singularities in the electronic dispersion of
two-dimensional systems that occur when the Fermi surface changes topology,
using catastrophe theory. For systems with up to seven control parameters
(i.e., pressure, strain, bias voltage, etc), the theory guarantees that the
singularity belongs to to one of seventeen standard types. We show that at each
of these singularities the density of states diverges as a power law, with a
universal exponent characteristic of the particular catastrophe, and we provide
its universal ratio of amplitudes of the prefactors of energies above and below
the singularity. We further show that crystal symmetry restricts which types of
catastrophes can occur at the points of high symmetry in the Brillouin zone.
For each of the seventeen wallpaper groups in two-dimensions, we list which
catastrophes are possible at each high symmetry point.
