Floer homology for dynamical systems, connecting it with Conley theory.
Jürgen Jost (Max Planck Institute)

Floer theory is a refinement of Morse theory that constructs a boundary operator by counting gradient flow lines between critical points of index difference 1 of a Morse function. This strategy can be extended to dynamical systems with periodic or homoclinic orbits, providing a link to Conley theory.