Division of Joint Research of
Geometry and Natural Science

In the pure mathmatics, there are three research fields of the Algebra, the Analysis and the Geometry mainly. In the geometry, there are three fields of the differential geometry, the topology and the Algebraic Geometry.

The differential Geometry is the field researching the space (which is called a manifold) where can treat the continuity and the differentiabiliy of various geometric quanttities and researching the properties of the figures in the space which are invariant under some Lie group action (on the space). The topology is the field researching the space (which is called a topological space) where can treat only the continuity of various quantities and researching the properties of the figures in the space which are invariant under continuous deformations. The algebraic geometry is the field researching the properties of the figures given as the common zero-point set of some polynomials. The purpose of this division of research is to construct the comprehensive geometric theory of the natural science (in wide sense) of the quantum mechanics, the condense matter theory, molecular biology, the grain boundary structure theory and composite materials mechanics, and feedback to each of the above fields of the natural science. This division was started from April 1st in 2025 for the above purpose.

Professor Naoyuki Koike (Director of DGNS)