I am mainly working on “free probability theory” and related fields.  How I came to this research field? The story goes back to high school. Originally, I was interested in physics and mathematics in high school. In high-school physics there were no differential equations. As soon as entering university, however, numerous differential equations appeared in physics. So, naturally, I got interested in differential equations, and also probability theory because the latter appeared in statistical mechanics and quantum theory.  Later, I started master’s and then, affected by the research group I was belonging to, got interested in free probability, which is connected to quantum physics from various aspects. Meantime, differential equations were rather out of scope of my research. However, in recent few years, I had a chance to work on a problem on engineering called “shape optimization” or “topology optimization”, in which partial differential equations (PDEs) are effectively used. Accordingly, I wrote research papers about these subjects using PDEs (including results with quite a mathematical rigor) and even received two paper prizes for them. Thus, I could achieve, with pleasure, my old dream of working on differential equations.

When I was an undergraduate student, I was interested in physics and mathematics. Emphasis of study was put rather on physics, and the study of math was limited to analysis because time was not enough to cover all the fields of math (and algebra and geometry were too tough for me at that time …).  In particular, I was interested in differential equations and probability theory because they appeared in various fields such as fluid mechanics, statistical mechanics and quantum theory. For example, probability theory in math was developed strongly motivated by physicist’s work (Einstein, Langevin,… ) on Brownian motion, and it is closely related to parabolic / elliptic partial differential equations; such a connection between physics and math interested me so much.  Studying these fields with great eager was an important step that led me to becoming a researcher.

In order to study stochastic differential equations that appear in statistical mechanics (in particular, the Langevin equation), I tried to read the book of Karatzas and Shreve’s “Brownian Motion and Stochastic Calculus”, but it was too difficult for me to understand. Then a senior colleague kindly helped me, providing important techniques behind, so that I could finally read the book until satisfactory part. For PDEs, I tried to read Gilbarg and Trudinger’s “Elliptic Partial Differential Equations of Second Order”, which again turned out too difficult for me.  Several years later, I started my PhD, and then I tried again this book. This time, I could read through without much difficulty.  There were other similar experiences: once a book was too difficult to read, but later it became rather easy to read. This kind of interesting experience still remains as a memory of having fun in studying.