**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.

Tokyo Metropolitan University