We shall start with an introduction to contact geometry, assuming no prerequisites. For those familiar with symplectic geometry or dynamical systems, a contact form is roughly an integral of a symplectic form. Precisely, a contact form on an (2n+1)-dimensional manifold is a 1-form a so that the wedge product of a with the nth power of da is never zero. In the right system of local coordinates (z, x₁, y₁, x₂, ..., y_n) the contact form always looks like

In other words, a contact form is a very "soft" geometric structure of the type made popular by Gromov in his book Partial Differential Relations. We shall show how a degenerate parabolic system of equations may be introduced, along with cut-and-paste methods, to construct a contact form. This is a joint effort with Hansjoerg Geiges and Matthias Schwarz, but it's mostly a report on work of Steve Altschuler and Lan-Fan Wu.
 

Convenors:Klaus Ecker, Alan Pryde