We study geometric objects like manifolds and knots from diverse viewpoints. We also visualize geometric concepts using computer, obtain new algorithms, and apply them to information science.

On the basis of research on various types of algebraic systems, we perform fundamental research and education on mathematics related to "structured information" bilaterally, towards information science, and from information science back to mathematics.

We aim to build a base to research nature's hidden laws, by carrying out education and research aimed at elucidating a variety of natural phenomena using analytic methods including construction of mathematically supported numerical methods, and intensive use of a computer.

The mathematical structure of large-scale systems has been studied by using computers, in fields such as statistical physics. In addition to these existing probabilistic approaches, we conduct studies searching for new mathematical structures, through education and research with an emphasis on the analysis of algebraic structures. Specifically, we aim to build up an algebraic theory related to image processing through these studies.

Through the process of setting and solving scientific issues by computer experiments, we are promoting education and research related to the construction of mathematical modeling and computer models. Moreover, by the process of setting and solving problems we aim to building a new theory of computational mathematics.