In breakthrough work, Sommese, Verschelde and Wampler
have initiated the new area of Numerical Algebraic Geometry.
In this talk I will describe recent progress in Numerical Geometry
of Partial Differential Equations (Numerical Jet Geometry).
The key tools are the continuation methods of Sommese,
Verschelde and Wampler, where generic points on the components of
the PDE are cut out by intersections with random linear spaces.
This is joint work with Jan Verschelde and Wenyuan Wu (UWO).