砂田 利一

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研究者氏名
砂田 利一
 
スナダ トシカズ
所属
明治大学
部署
総合数理学部
職名
専任教授
学位
理学博士(東京大学), 理学修士(東京大学)

プロフィール

(Excerpt from the survey article "An Overview of Sunada's work" written by A. Katsuda and P. W. Sy)

Professor Toshikazu Sunada was born in Tokyo, Japan, on September 7, 1948, three years after the end of World War II. He dwelled and grew up in the suburb of Tokyo until the age of twenty-five. Sunada described himself in his childhood as an ordinary boy, somewhat introverted and showing no particular interest in any subjects taught in primary and junior high schools. According to his reminiscence, he sat absentmindedly all day long during class hours. He even confessed that arithmetic was then his instinctive dislike.

His zest for mathematics arose when he was a high school student and had a chance to read "History of Modern Mathematics" written by Takagi Teiji, a Japanese luminary who established the class field theory, a culmination of algebraic number theory. The book, including a vivid description of the lives of Gauss, Abel, and Galois together with the development of the theory of elliptic functions, was so fascinating that it led him to the ambition of becoming a mathematician. Since he had thought of himself as a literature-oriented person at that time, this was a major turning point in his life.

He thus decided to study mathematics and entered Tokyo Institute of Technology (TIT), which had a department of mathematics of moderate size. However, soon after his admission to the university (1968), his study was disrupted by student riot, a movement sweeping over universities around the world. During this period, classes were cancelled and the campus was locked out. Interested students of the mathematics department voluntarily requested their teachers to organize seminars outside the campus. The subjects they took up then were vector bundles and complex multiplications; topics which were not covered in the regular lectures for undergraduate courses. The enthusiasm for mathematics that the teachers demonstrated as well as their selfless effort to impart knowledge even in this extraordinary period has left a lasting impression on the mind of the young Sunada. This experience made him more ambitious to become a professional mathematician. When Sunada was in his senior year, his supervisor was Prof. Koji Shiga, who conducted one of the seminars mentioned above and is now Sunada's lifelong friend.

After his undergraduate studies, he was admitted to the graduate school of the University of Tokyo (UT) and soon began his research under the supervision of Prof. Mikio Ise. The most decisive moment for his future career came when he defended his master's thesis which consists of three different subjects in front of an examination committee. Since the time allocated for presentation to each student was short, he had to choose one out of the three subjects. Prof. Kunihiko Kodaira, a Fields Medal laureate, asked Sunada to explain in detail the other two subjects as well, even though his time was already up. Moreover, Kodaira made valuable comments to each subject. This happening was a big boost to Sunada's confidence in pursuing his dream.

Just after receiving his master's degree from UT in 1974, he was appointed as a research associate at Nagoya University (NU) where he was to stay for the next 15 years. This stay has made his dream to become a mathematician comes true. In 1977, he received his doctorate degree by submitting a dissertation to UT. In 1979-80, he was invited as a guest researcher at Bonn University. He says that the two-years stay in Bonn was the most fruitful time in his life. During this period, he made the aqcuaintance of many active young mathematicians, and published a series of excellent papers. And it was also during this period that his geometric model of number theory was conceived.

After his return to NU, he was promoted to associate professor in 1982. In 1985, he gave a beautiful construction of isospectral manifolds based on his geometric model of number theory. For this important contribution, he was subsequently awarded the Iyanaga Prize by the Mathematical Society of Japan in 1987.

Sunada became a full professor at NU in 1988. Three years after, he was appointed professor at UT (1991-1993) and thereafter, at Tohoku University (TU, 1993-2003) before he has finally settled down at Meiji University in 2003. Currently he is also professor emeritus of TU, a position held since 2003, and is affiliated with the newly-established Meiji Institute for Advanced Study of Mathematical Sciences in Tokyo. It is a rare case in Japan that a full professor transfers frequently from one university to another since there is almost no difference in the financial status.

The motivation for his frequent movement was to seek better research environment. He frankly says "UT, one of the most prestigious universities in Japan, was worst in my experience as far as the human relation is concerned". In the meanwhile, Sunada stayed for six months (1988) in Institut Hautes Etudes Scientifiques (IHES) as a guest professor, for a few months in Isaac Newton Institute at Cambridge as an organizer of a special project (2007), and for seven months in Max Planck Institute in Bonn (2008) as a visiting professor. In 2008, he held an Andrejewski Lecturership at Humboldt University in Berlin under the auspices of the Walter and Eva Andrejewski Foundation as a distinguished scholar. He also stayed in Mathematical Sciences Research Institute (MSRI) in Berkeley, Johns Hopkins University, Augsburg University, Institut Henri Poincar´e (IHP), Tata Institute of Fundamental Research, Institut Mittag-Leffler, the Academy of Science in Beijing, National University of Singapore, and the University of the Philippines for short periods. His first stay in the Philippines (1986), which was the most exciting moment in all of his travels (where he has witnessed the peaceful People Power Revolution in Manila), was the beginning of his active involvement in the Southeast Asia regional mathematical activities.

Sunada gave an invited lecture at the International Congress of Mathematicians (ICM) in Kyoto in 1990, at the Third Asian Mathematical Conference (AMC) in Manila in 2000, and at the LMS South West and South Wales Regional Meeting in Cardiff, UK in 2007, to name a few. He was invited to numerous other international conferences and symposia as a keynote speaker.
His activities are not limited to teaching and research. He was chosen a member of the Kyoto Prize Selection Committee for three terms (1989, 1994, 2002) in the past 20 years. In 2008, he was appointed a panel member of the European Research Council, an organization set up to promote outstanding, frontier research in all areas of science and humanities throughout Europe.

His other services to the mathematics community include his two-term board membership of the Mathematical Society of Japan and the membership of the IMU-CDE committee where he served for two consecutive terms. Moreover, he helped in the organization of several major conferences, including the celebrated Taniguchi Symposia, held in Asia as a member of steering, scientific or advisory committee.

Besides his many research publications, Sunada has written a number of mathematics books for the general public as well as textbooks for undergraduate and graduate students (most of which are in Japanese) and enlightening essays which appeared in Sugaku Seminar (Mathematics Seminar) and other mathematical magazines. He has also been involved in the publication of several series of mathematical books, journals, and proceedings as an editor. Sunada is at present a member of the Editorial Board of a popular Japanese mathematical magazine, Have Fun with Mathematics, published by Kame-Shobo.

Although Sunada usually portrays himself as a geometer, we realize from his list of publications, that it is difficult to single out his specialization. In fact, Sunada's work covers complex analytic geometry, spectral geometry, dynamical systems, probability, and graph theory. Through his work, we would describe him as an extraordinary and talented man with enormous insight and technical power who is constantly generating new ideas and methods to form exciting and remarkable mathematical results.

研究分野

 
 

経歴

 
2015年5月
 - 
2015年6月
The Issac Newton Institute, University of Cambridge Visiting Fellow
 
2009年1月
 - 
2009年3月
Institut des Hautes Etudes Scientifiques (IHES) Visiting Professor
 
2008年9月
 - 
2008年12月
Bielefeld University Visiting Professor
 
2008年4月
 - 
2008年9月
Max Planck Institute in Bonn Visiting Professor
 
2002年11月
 - 
2002年12月
Mittag Leffler Institute, Sweden Guest Professor
 

学歴

 
 
 - 
1974年3月
東京大学 理学研究科 数学
 
 
 - 
1972年3月
東京工業大学 理学部 数学科
 

委員歴

 
2017年4月
 - 
現在
一社)数学教育学会  特別顧問
 
2014年
 - 
2015年
Scientific Advisory Committee of the special project ''Periodic and Ergodic Spectral Problems'' at Isaac Newton Institute for Mathematical Sciences  Committee member
 
2013年
 - 
2014年
Program Committee (Geometry Section) of ICM 2014  member
 
2010年
 - 
2015年
「プリンストン数学集成」編集委員会  委員長
 
2010年
 - 
2014年
ヨーロッパ科学評議会  専門委員
 

受賞

 
2017年4月
藤原洋数理科学賞
 
2013年3月
日本数学会出版賞
 
1988年
Mathematical Society of Japan 日本数学会弥永賞
 

論文

 
From Euclid to Riemann and thereafter
Proceedings for the conference "Geometry in History"      2017年2月   [査読有り][招待有り]
Topics on mathematical crystallography
T. Sunada
London Mathematical Society Lecture Note Series   436 475-519   2017年   [査読有り][招待有り]
In July 2012 the General Assembly of the United Nations resolved that 2014 should be the International Year of Crystallography, 100 years since the award of the Nobel Prize for the discovery of X-ray diffraction by crystals. On this special occasi...
Standard 2D crystalline patterns and rational points in complex quadrics
Southeast Asian Bulletin of Mathematics   38 731-750   2014年12月   [査読有り]
A certain Diophantine problem and 2D crystallography are linked through the notion of standard realizations which was introduced originally in the study of random walks. In the discussion, a complex projective quadric defined over Q is associated ...
Japan. J. Math.   7 1-39   2012年3月
This is an expository article on modern crystallography
based on discrete geometric analysis, a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability, which has been developed in the la...
Tatsuya Tate
Jornal of Functional Analysis   262 2608-2645   2012年1月
This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the 'normalized' position of the walk. When the position is in the support of ...

Misc

 
Geometric Aspects of Large Deviations for Random Walks on a Crystal Lattice
小谷元子
数理解析研究所講究録   1236 112-114   2001年
Book Review in Bull. Amer. Math. Soc. "Random walks on infnite graphs and groups" by W. Woess
Bull. Amer. Math. Soc.   39 281-285   2001年   [査読有り]
跡公式とLaplacianのspectrum
数学   33(2) 134-142   1981年4月
幾何学における数論的方法について --zetaおよびL-関数の幾何学的類似とその応用--
数学   38(4) 289-301   1986年12月
マニラの熱い日々、-数学者の見たフィリピン-
数学セミナー   32-35   1986年

書籍等出版物

 
基本群とラプラシアン
紀伊国屋書店   1988年   
"行列と行列式I, II"
岩波書店   1988年   
"幾何入門I, II"
岩波書店   1996年   
曲面の幾何
岩波書店   1977年   
高校生に贈る数学III
志賀浩二 (担当:共著)
岩波書店   1996年   

講演・口頭発表等

 
Isospectral manifolds [招待有り]
1984年6月   
Isospectral manifolds [招待有り]
6th Differential geometry and differential equations   1985年6月   
Ihara zeta functions [招待有り]
Annual Meerting of Mathematical Society of Japan   1987年4月   Mathematical Society of Japan
Lectures on twisted Laplacians [招待有り]
1990年2月   Tata Institute
Trace formulae in spectral geometry [招待有り]
International Conference of Mathematics (ICM) in Kyoto   1990年8月   

Works

 
解説ー「若き数学者への手紙」文庫版
その他   2015年7月
岩波 世界人名大辞典
その他   2013年
解説--「数学と算数の遠近法──方眼紙を見れば線形代数がわかる」
その他   2010年11月
数学・哲学・言語学研究所訪問記/特集・21世紀の数学をふりかえって
その他   1996年
往復書簡「純粋数学vs 応用数学」
その他   1994年

競争的資金等の研究課題

 
離散幾何解析学の進展(代表)
文部科学省: 基盤研究(A)
研究期間: 2015年4月 - 2019年3月    代表者: 砂田利一
離散幾何解析学の展開(代表)
文部科学省: 基盤研究 (B)
研究期間: 2012年4月 - 2015年3月    代表者: 砂田利一
離散解析幾何学の発展と応用(代表)
文部科学省: 基盤研究 (B)
研究期間: 2009年4月 - 2012年3月    代表者: 砂田利一
非可換幾何解析学の研究(代表)
文部科学省: 基盤研究 (C)
研究期間: 2006年4月 - 2008年3月    代表者: 砂田利一
可換及び非可換ブロツホ理論(代表)
文部科学省: 基盤研究 (A)
研究期間: 2001年4月 - 2005年3月    代表者: 砂田利一