Yuya Koda - Appointed in AY2023

While studying mathematics at university, I encountered a field called topology, which I have been researching ever since. Unlike high school (or entrance exam) mathematics, which is a competition to solve problems quickly, the mathematics you major in at university emphasizes accurately grasping abstract concepts and understanding their interrelationships. Many people are taken aback because it is qualitatively different from the mathematics learned up to high school, but the academic style of steadily building understanding from the ground up suited me well. By learning mathematics, I felt the joy of acquiring a new language, which opened up a world that I could perceive and explore. I have fond memories not only of studying alone outside of classes and seminars but also of the seminars I attended that transcended academic years and universities. In the process of learning mathematics, I had the exhilarating experience of suddenly being able to solve difficult problems that were once completely beyond me. But more than that, I realized that there were countless fascinating problems that I could not have even imagined before I started studying. I chose my current research field because it was the one that shone brightest among the landscapes that began to vaguely appear to me at that time.

My research specialty is the topology of manifolds. A manifold is a major spatial model used in mathematical research and is a generalization of the vector spaces you learn about in your first year. Incidentally, John Nash, who won the Nobel Prize in Economics, also has famous achievements in the study of manifolds. Topology is the field that treats space as something pliable and studies its general shape. This field contains many simple, intuitively understandable concepts, such as knots and surfaces. Its appeal lies in the fact that this simplicity allows it to be studied from various perspectives using a wide range of mathematical methods. Recently, topological methods have been attracting attention not only in the natural sciences like physics, biology, and chemistry, but also in information science and statistics.

I hope that you will cultivate a broad perspective and objectivity through diverse encounters and learning experiences. Furthermore, I hope you will also acquire a specialization if possible. When you acquire specialized knowledge, you may find that reasoning or minor discoveries that seem perfectly ordinary to you appear novel and original to others. Conversely, experts sometimes unconsciously utter highly valuable insights, so people who can recognize the useful information contained within and utilize it are also important. Even in pursuing that goal, I believe the deep learning you undertake during your student life will prove invaluable.