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:
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.