The concept of nonlinear structure, a main focus of our program, represents a structure that exists not only behind such geometric subject as a curved space as well as other mathematical phenomena where, for instance, a doubled input may not yield a doubled result. Nonlinear structure plays a key role in mathematics, natural sciences, engineering, social sciences and other academic disciplines.

Our program investigates *nonlinear structure* through the
following three perspectives, with a particular emphasis on the notion
of *singularity:*

**Nonlinear Equation****Discreteness and Continuity****Symmetry of Structure**

Our primary objective is to build a solid
mathematical foundation for nonlinear structure research and create
stronger ties with researchers in other relevant fields. We are also
committed to laying the mathematical groundwork for wide range of research areas, including computer
vision, mathematical physics, and crystal growth. Another key goal is to
discover new approaches to some areas of pure mathematics, such as
algebraic geometry and representation theory.

Through this research program, we seek to **build stronger
connections with other institutions in and outside of Japan**, **educate young
researchers, and improve and expand our literature and intellectual property services**.