[No. 132] Yoshitsugu Yamamoto

I will look back on my time as a graduate student at Keio and my 38 years as a faculty member at Keio University, Tokyo Institute of Technology, and the University of Tsukuba.

As I entered my final year of undergraduate studies, I decided to go to graduate school out of a desire to study more, and I took the entrance exam for the Department of Industrial and Systems Engineering. On the day of the exam, the results of the written test were announced in the morning, and interviews for those who passed were scheduled for the afternoon. I had overslept and rushed to the Yagami Campus without even shaving. I found my exam number and went in for the afternoon interview. I still remember Professor Tatsuo Kawata's comments on my exam paper and the gentle smile of Professor Yoshio Hayashi, who served as the moderator.

After enrolling, I was accepted into Professor Tomoaki Sekine's laboratory. I started from a point where I had no idea what my senior lab members were talking about when they asked if I knew about Kuhn-Tucker or fixed points. The lab had more seminars than classes, and it became painful to listen when I couldn't understand the content. So, I ambitiously decided to understand every seminar from then on. During the summer break, a friend and I secluded ourselves at a hot spring inn deep in the mountains of Nagano to restudy fundamental mathematics, preparing for the seminars that would start in the fall. I still can't forget the taste of the *koi no arai* (sliced raw carp) we ate then.

I am grateful for the good fortune of having had such experiences: Professor Tatsuo Kawata, who would appear in the classroom as if guided by the fragrant aroma of his pipe, saying, "A proof is just a matter of writing down the obvious"; the lecture materials from Professor Jiro Yamauchi, whom we affectionately called "Ojiichan" (Grandpa), filled with handwritten numbers; and the reprimand from Professor Tomoaki Sekine, "I have no idea what you're talking about."

After advancing to the Doctoral Programs, I went through a period of fumbling in the dark. I would attend study groups held at the Central Research Institute of Electric Power Industry, be dazzled by the new research findings of those around me, and then feel dejected every day, keenly aware that I had nothing to show for myself. Nevertheless, I climbed the hill to Yagami every day, thinking of Professor Sekine's office as if it were my own.

Though it would be unheard of these days, I was fortunate enough to be hired as an assistant in the Department of Industrial and Systems Engineering before obtaining my degree, and I was swamped with writing my doctoral dissertation and preparing for classes. Shortly thereafter, I received an offer from Tokyo Institute of Technology. I left the Yagami campus behind, looking back on the hill I had climbed up and down for over six years—five as a graduate student and one year and three months as an assistant.

At Tokyo Tech, I had the opportunity to assist Professor Masakazu Kojima, my senior from Keio, with his research on fixed-point algorithms. My days were spent reading the papers that poured in from researchers overseas and striving to produce results that would surpass them. This type of algorithm has the desirable feature that its convergence does not depend on the local properties of the function, but improvements in computational speed were needed, and several types of algorithms had been proposed. We aimed to construct a fundamental structure that could provide a unified understanding of these algorithms. Those were happy days, completely absorbed in research.

After a few months, a professor from the University of Tsukuba asked if I would be interested in joining as a lecturer. I later visited the campus and was overwhelmed by its vastness. At that time, I lacked the confidence to move to Tsukuba and continue my research on my own. For a month, I agonized between the desire to continue my research in my current environment and the idea of starting a new life in Tsukuba. However, with the recommendation of Professor Sekine, who had mentored me during my student days, I decided to move to the University of Tsukuba. Thus, in the fall of 1980, I bid farewell to my life in Ookayama.

At that time, Tsukuba was a frontier—an artificial city that had appeared in a vast pine forest, with the Joban Line from Ueno as its only means of public transportation. While it was a geographical outpost, its residents were young and filled with the enthusiasm of being at the forefront of Japan's science and technology research. The College of Policy and Planning Sciences at the University of Tsukuba, where I was appointed, was a huge organization. However, I launched the Mathematical Engineering Laboratory, where I could freely discuss various research fields with colleagues who were also interested in optimization research. I continued my work on fixed-point algorithms from my Tokyo Tech days and also began to tackle the existence proof and computation of competitive equilibria in economies with indivisible goods. It was thanks to my position in an organization like the College of Policy and Planning Sciences, which aimed for interdisciplinary research, that I was able to pursue such studies.

Later, with the support of the Humboldt Foundation, I was able to stay at the University of Bonn in what was then West Germany and conduct research on the generalization of Sperner's lemma and on variational inequalities. I am grateful to the College of Policy and Planning Sciences at the University of Tsukuba for allowing me to take a two-year research leave, and I fondly recall the privileged environment that academics enjoyed at that time.

I am grateful that a person of my limited talents was able to stand on the lecture platform and continue research for 38 years, all thanks to my respected mentors, trusted research colleagues, and brilliant students.