Graduate School of
Science and Engineering

A river can be regarded as a bundle of flow lines. Foliations are abstract generalization of such geometric structures. Namely, a foliation on a space is a decomposition of the space into spaces of smaller dimension. I am interested in the geometry and topology of foliations. They have been studied in these 50 years originally motivated by the research on partial differential equations and dynamics on 2-dimensional spaces. The relation of foliation theory to 3-manifolds, group actions and differential geometry is also actively studied. I am investigating global geometric properties of foliations from the viewpoint of cohomology and characteristic classes. The goal of my recent research is to understand mysterious phenomena on foliations called “rigidity”, which means that certain special foliations with large symmetry have distinguished dynamical properties.