Takashi Tsuboi

I have been pursuing a career as a geometer. Earlier in my career my interest was classifying the topology of manifolds as well as the structures on manifolds. Recently, I began working in interdisciplinary mathematical research, and I have now joined the Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) at RIKEN, directed by Tetsuo Hatsuda. iTHEMS is an international research program that promotes close collaboration between researchers from different disciplines through mathematics.

During the 20th century, mathematics became more abstract and more formal, which influenced me when I was a student; however, around the end of the 20th century, many mathematicians focussed again on the applications of mathematics. This transition occurred because the range of applications for mathematics became much larger as a result of the abstraction and formalization of mathematics on the one hand, and the development of computers, which enabled mathematicians to carry out mathematical experiments more easily, on the other hand. For example, measure theory and probability theory in mathematics are now well understood by mathematicians and form the foundation of its application, together with traditional analysis and linear algebra. Major mathematical problems were usually formulated completely within the discipline of mathematics in the middle of 20th century, but now more and more mathematical problems appear in other fields of science.

Areas of research—including symplectic structures, Floer theory, and the moduli spaces of Riemann surface, which are related to my research field in geometry—are investigated in close relationship with physics, and persistent homology certainly has applications in material sciences. Many interesting problems are being presented to mathematicians and new research fields are expected to arise. The shapes of macromolecules as well as the processes involved in their generation are interesting subjects and their study would be related to low (2, 3 and 4) dimensional topology. I am interested in these fields as they are interdisciplinary fields close to my area of focus.

Interdisciplinary mathematical research includes diverse fields of science. It is important to conduct research actively in all of these fields and advance them.

In order to do so, we need to promote interaction between the most advanced mathematics and research in other fields of sciences and industry and generate synergies among them. We hope to achieve significant results from the fusion of fields as well as new developments in mathematics and other fields of science. It is also important to raise public awareness of the value of interdisciplinary mathematical research. In order to promote interdisciplinary mathematical research, we would like to train young people so that they lead the next generation to promote collaboration between mathematics and other fields of science as well as with industry.

Research questions can be discovered in everyday conversations. Together with my colleagues in iTHEMS, I would like to create at RIKEN an atmosphere of openness that naturally facilitates the communication of ideas and interesting new theories.