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I study topology of 3 and 4 dimensional manifolds, using moduli spaces of solutions to partial differential equations which come from gauge theory. We can construct differential topological invariants of 4manifold from the moduli spaces. In general, it is difficult to calculate the invariants. But if you cut the 4manifold along 3manifolds and split it into smaller 4manifolds, the calculation of the invariants becomes easier. In the procedure, Floer theory of 3manofolds plays an important role. Currently I study SeibergWittenFloer stable homotopy type of 3manifolds.
Keywords  Topology, Gauge Theory, Floer Theory 

Faculty , Department  Faculty of Mathematics , Department of Mathematics 