Hiroshi Kawabi - Appointed in AY2018

I have liked mathematics since high school, but I was particularly struck when a teacher in my probability and statistics class said, "Probability theory is a part of analysis." At the time, I was also interested in how mathematics was applied to other fields, so when I was choosing my future path, I consulted that teacher. He advised me to study mathematical economics in the Faculty of Economics, so I enrolled in the Faculty of Economics. While I feel I wasted some time as a student at Hiyoshi, not being very interested in economics lectures, after moving up to the Mita campus, I joined a mathematical economics seminar. Inspired by the brilliant senior students in the seminar, I began studying general equilibrium theory and its related mathematics. In the end, I found mathematics more interesting and switched to it in graduate school. In graduate school at Yagami, I was dabbling in research on partial differential equations related to the calculus of variations, continuing my undergraduate studies in analysis. However, one day, I casually attended a geometry seminar and was deeply impressed to learn that probability theory was being applied to various problems in partial differential equations and geometry as analysis on path spaces. After much thought, I decided that this was what I really wanted to do, and I left Keio to study probability theory in earnest under the professor who had given the seminar. After that, I was fortunate to have encounters with people in various places both in Japan and abroad, and by weaving these experiences together, I ended up on the path of research in probability theory.

Probability theory is a field where one can be conscious of its connection to applications, as it is widely used not only in physics, such as statistical mechanics and quantum mechanics, and biology, but also in finance theory and theoretical economics. Among these, the theory of stochastic integrals and stochastic differential equations, founded during World War II by the Japanese mathematician Kiyosi Itô to mathematically and rigorously understand stochastic phenomena that change moment by moment with the addition of noise like Brownian motion, continues to develop today as the research field of stochastic analysis. This research field also has the aspect of being analysis on an infinite-dimensional space called a path space, by treating the solutions of stochastic differential equations as functionals of Brownian motion. I believe I specialized in probability theory because I found this way of thinking fascinating as a graduate student. On the other hand, it is well known that the limit of a spatio-temporal scaling transformation of a simple random walk becomes Brownian motion. Through this concept of a scaling limit, probability theory is also actively used as an effective tool for geometry and analysis on discrete spaces. In recent years, I have been studying random walks on discrete models with periodicity, such as crystal lattices and nilpotent covering graphs, and investigating the solutions of stochastic differential equations and the long-time asymptotic behavior of heat kernels, which can be understood as scaling limits. I also find it interesting that the quantities appearing in some of the limit theorems obtained can be understood through a variational principle. Looking back now, perhaps this sensibility was cultivated through my studies of theoretical economics as an undergraduate.

I think it's a good idea to immerse yourself completely in whatever you find interesting during your time at university, not limited to economics. The Keio Faculty of Economics should have the breadth to accept that. Furthermore, since Keio is a large comprehensive university, its students come from a wide variety of hometowns. While students from regional areas will be stimulated by their new life in Tokyo and broaden their horizons, I hope that students from the Tokyo area, including those who advanced from within Keio's affiliated schools, will also actively interact with students from other regions and learn to think about things from multiple, non-Tokyo-centric perspectives. I've written some rather formal things, but above all, please have a fulfilling university life and make friends you can stay in touch with even after graduation. They are a treasure for a lifetime.

(Interview conducted in December 2018)