Gromov–Witten invariants and Lagrangian Floer theory for compact symplectic manifolds are now very much established as far as general theory concerns. In symplectic geometry, non-compact symplectic manifolds (such as the cotangent bundle) are as important as compact ones. There are many versions and variants for non-compact Gromov–Witten–Floer theory and many of them are still not yet completely established. In this talk, I want to explain some of such versions and issues to study them.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/8493