Until now, I have tried to extend the geometry of nilpotent groups to the geometry of solvable groups. More precisely, I have studied the cohomology theory of homogeneous spaces of solvable Lie groups and complex geometry of non-Kähler manifolds. It seems that the gap between nilpotent groups and solvable groups is small. But this gap contains a potential for geometry. By the growing out of left-invariance and non-triviality of local system cohomology, I succeeded in giving a great surprise.
Recently, I am interested in the geometry which relates to reductive or semi-simple groups in contrast to nilpotent or solvable groups In particular, I study non-abelian Hodge theory, variations of hodge structures, lattices in semi-simple Lie groups and locally homogeneous spaces.