April 30, 2004: Chris Wendl, CIMS
Holomorphic Curves, Foliations and
Dynamics: How a PDE helps to solve an ODE problem
I will give an overview of my thesis problem, some
motivating ideas from
contact geometry (including the definition of "contact geometry"), and
the
eclectic mix of mathematical machinery that makes such problems
tractable.
The most important tools are pseudoholomorphic curves, a generalized
notion of analytic functions which combines complex analysis with heavy
doses of elliptic PDE theory, nonlinear functional analysis,
differential
geometry and topology. For good measure, this toolbox ends up
providing
answers to some quite nontrivial problems in Hamiltonian
dynamics. I
shall attempt to summarize this story at the level of the "typical
Courant
student who knows what a manifold is."
