# Message from the Dean of the Graduate School of Mathematical Sciences

Dean of the Graduate School of Mathematical Sciences

**Toshitake Kohno**

During their development, mathematics and various other sciences have always exerted a strong mutual influence. In the 17th century Leibniz and Newton developed differential and integral calculus, giving a language and method to describe the laws of dynamics in nature. It is also well known that the discovery of non-Euclidean geometry and differential geometry, developed by Gauss and Riemann from the middle of the 19th century, became the basis of Einstein's general relativity.

From the middle of the 20th century mathematics has been developed with highly abstract formalism. However, thanks to this development, mathematics has acquired a remarkable versatility, namely, it has been endowed with the possibility to be applied in various areas.

Nowadays, the different areas where mathematics is effectively used are extremely wide and we therefore require talents with broad viewpoints, if we wish to aim for the development of mathematics in relation with various other sciences.

The "Leading Graduate Course for Frontiers of Mathematical Sciences and Physics" (FMSP) is provided through the joint efforts of the Graduate School of Mathematical Sciences, the Department of Physics and the Department of Earth and Planetary Science of the Graduate School of Science together with the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo. The purpose of the FMSP program is to foster leaders for the next generation in research in mathematics, who are able to develop new research areas that transcend the boundaries of mathematics and various sciences, such as theoretical physics, and to create theories in advanced mathematics that contribute to these areas.

The FMSP program also aims to foster human resources with broad viewpoints, capable of making valuable contributions to problems raised in industry and environmental issues.

Nowadays, thanks to the synergy between mathematics and theoretical physics, new research areas have successively been created beyond the traditional boundaries. This may bring about a fundamental change in our view of the universe. What will eventually emerge for both mathematics and physics through this synergy is of course still uncertain. But what is certain is that there are great challenges ahead for the next generation. For environmental issues, for example, we need analysis of complicated behaviors of fluids and it is an important problem to develop a mathematical theory which is effective for these problems. Concerning problems in industry, we have obtained results by applying analytic methods called inverse problems, but we will need new techniques in mathematical sciences involving algebra and geometry as well.

For the purpose of contributing to the solution of problems in mathematics and the mathematical sciences in various areas, we need to have a global viewpoint, beyond the boundaries of research areas. From this point of view, in the FMSP program we organize transversal course works, seminars and tutorial workshops, removing traditional boundaries between disciplines.

We will also set up various occasions where students learn about problems in industry and work together on these problems.

The FMSP program aims at fostering talents that are competitive at the international level. We support our students to pursue research at institutions abroad for a longer period. Kavli IPMU offers an international research environment, where half of the researchers are from abroad. It will be a gateway to international experience for FMSP students to attend activities at Kavli IPMU and to discuss with researchers there.

We have been blessed with a promising start thanks to the participation of highly motivated students. We are ready to make a full effort to improve and enhance the program by organizing various activities.

It is our wish to provide our students, interested in mathematics and mathematical sciences, with a secure environment in which they can study, as well as with a broad range of opportunities for their future pursuits. We are very much looking forward to welcoming motivated students into our program.

July 2016

**Toshitake Kohno**

>>Message from the former Dean of the Graduate School of Mathematical Sciences