Time: 4:40 p.m.
Location: 106 McAllister Building
Name: Helmut Hofer
Affiliation: NYU
Title: Pseudoholomorphic Curves and Dynamics
Abstract: Hamiltonian dynamics on a three-dimensional energy surface is closely related to the theory of pseudoholomorphic curves. The moduli spaces of pseudoholomorphic curves are the ingredients of various flavors of symplectic field theory. One of these theories is embedded contact homology. Recent work of Taubes (in progress) shows that the latter is the same as Seiberg-Witten Floer Theory. As a corollary one obtains the complete Weinstein conjecture in dimension three. It seems that Hamiltonian dynamics is the place where several powerful theories meet and there is hope that these `new technologies' lead to new results about more general aspects of the dynamics. It is the purpose of the talk to describe some of the ideas.
