Floer Theory in Symplectic Topology

My research focuses on Floer theory in symplectic topology. Floer homology is a version of Morse homology for infinite-dimensional manifolds; in Lagrangian Floer theory, the infinite-dimensional manifold is a covering space of paths bounded by Lagrangian submanifolds in a symplectic manifold, and the Morse function is the symplectic area functional. Floer's chain complex is generated by the intersection points of Lagrangian submanifolds, and the differential counts pseudo-holomorphic strips. I am investigating Floer theory for Lagrangian immersions, Lagrangian submanifolds with Legendrian cylindrical end in symplectic manifolds with concave end, and more singular Lagrangian submanifolds in singular symplectic manifolds.

Favorite References

A. Floer, Morse theory for Lagrangian intersections, J. Differ. Geom. 28, No. 3, (1988) 513-547.
H. Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. math. 114 (1993) 515-563.