We study differentail geometry, symplectic geometry, and algebraic geometry. Distinctive characters and uniform aspects of these geometries, especially octonions, are main motives for our researches.
The researches have been successfully performed in the geometry of manifolds with special holonomies, comparative study of polytopes and complex surfaces along the representations of exceptional Lie groups. Therefrom, we contribute to construct new geometric spaces and to produce creative comparative studies among them. These were published in Advances in Mathematics and Transactions of the American Mathematical Society.