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I am a geometer and have been studying the following subjects:

1) Let G/H be a homogeneous space. If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. I am studying the existence problem of compact Clifford-Klein forms of non-Riemannian homogeneous spaces mainly from the cohomological viewpoint.

2) Conley index is a homotopical invariant in the study of topological dynamical systems. I proposed a new, simpler framework for Conley index theory.

Roughly speaking, my main interest is to study problems in various areas (such as Lie group theory, differential geometry, dynamical systems) from the perspective of homotopy theory.