Return to Colloquia & Seminar listing
Counting holomorphic curves: "hard" results in symplectic geometry
Colloquium| Speaker: | Michael Sullivan, University of Michigan |
| Location: | 693 Kerr |
| Start time: | Thu, Jan 30 2003, 4:10PM |
Description
Gromov's work in the mid-eighties on holomorphic curves
in symplectic manifolds has since led to the development
of many geometrical ("hard") results in a theory
once considered "soft." In the late eighties, Floer
develop a symplectic invariant, now known as
Floer homology, which counts certain holomorphic curves.
This invariant has proved to be quite useful; for example,
it was used in the proof of the Arnold Conjecture for
Hamiltonian dynamics.
Contact geometry is the odd-dimensional analog to
symplectic geometry. Despite the similarities between
the two fields, only recently have "hard"
results emerged using Floer-type counts of holomorphic curves.
I will survey some of these results, including a
computation (joint with M. Hutchings) which conjecturally
recovers Seiberg-Witten-Floer homology, a useful tool
in four-manifold theory.
3:45 Refreshments will be served before the talk in 551 Kerr Hall