7 February

**Joel Fish**UMB

Title:

*Feral curves and minimal sets*

ABSTRACT:I will discuss some current joint work with
Helmut Hofer, in which we define and establish
properties of a new class of pseudoholomorhic curves
(feral curves) to study certain divergence free
flows in dimension three. In particular, we show
that if \(H\) is a smooth, proper, Hamiltonian in
\(R^4\),
then no energy level of \(H\) is minimal. That is, the
flow of the associated Hamiltonian vector field has
a trajectory which is not dense.