Inter-universal Geometry Center 宇宙際幾何学センターIUGC

About IUGC

IUGC (Inter-universal Geometry Center) is a research institute promoting the dissemination and development of Interuniversal Teichmüller Theory (IUT Theory). IUT theory is expected not only to solve the ABC conjecture, the ultimate conjecture of modern number theory, but also to apply to many other important problems.


The Inter-universal Teichmüller theory (IUT theory) was publicly announced in 2012 by Professor Shinichi Mochizuki from Kyoto University. It is an important theory with numerous new concepts and ideas. The papers on this theory were published in a special issue ( of Publications of RIMS in 2021. The main prerequisite of IUT is algorithmic anabelian geometry, which has been primarily developed in Japan since 1995. Despite significant efforts made between 2015 and 2021, including multiple international IUT workshops that increased the number of IUT experts to over 15 from more than 5 countries, the theory has been unable to follow the usual process of dissemination due to various unfortunate circumstances. As a result, many countries still lack communities of experts in this theory. We are committed to sincerely addressing this situation as our starting point.


IUGC Director Kato Fumiharu

The Inter-universal Geometry Center (IUGC) was born from the desire to spread awareness of the novelty of the Inter-universal Teichmüller theory (IUT theory) to a wide audience , engage more people in the development of new mathematics using IUT theory, and ultimately enrich modern mathematics.

Research on the IUT theory is primarily centered at the Research Institute for Mathematical Sciences (RIMS), Kyoto University, where Professor Shinichi Mochizuki, the theory’s founder, is based. However, in order to pursue new directions that encompass synergistic effects with conventional mathematical theories, it would be beneficial to have an organization that operates independently with its own management structure and mindset. This approach would enable us to bring about a new phase in the dissemination and development of the IUT theory, and potentially drive further advancements in modern mathematics as a whole.
These are the basic principles, on which we understand the role of our research center.

The goal of promoting modern mathematics, particularly IUT theory and its related fields, implies an important viewpoint that extends beyond research promotion. It also encompasses redefining the manner in which theoretical research is conducted in contemporary society. With this perspective in mind, the IUGC aims to organize and support diverse activities that facilitate the dissemination of theoretical research to society, as well as contribute to the career development of researchers and the reciprocal exchange of knowledge and expertise.