Modern geometry is aimed at mathematically formulating spatial concepts and carrying out research on spatial properties. For instance, the earth that we live in is a typical geometric object. An object like this is mathematically referred to as a manifold. The primary purpose of our research is to determine the geometric properties of a manifold, configure geometric invariants of that manifold, and use this information to characterize its space. Specific fields include noncommutative differential geometry, the three-dimensional Poincare conjecture, the index theorem of an operator, gauge theory and four-dimensional manifold theory, the distribution of the characteristic roots of a differential operator, and so on.

Fields of study ; Differential geometry, topology, global analysis, low-dimensional topology, manifold theory, operator algebra