Sunada Toshikazu

J-GLOBAL         Last updated: Nov 22, 2018 at 03:23
Sunada Toshikazu
Meiji University
School of Interdisciplinary Mathematical Sciences
Job title
Dr. of Science(The University of Tokyo), Master of Science(The University of Tokyo)
Research funding number


(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.

Research Areas


Academic & Professional Experience

May 2015
Jun 2015
The Issac Newton Institute, University of Cambridge Visiting Fellow
Jan 2009
Mar 2009
Institut des Hautes Etudes Scientifiques (IHES) Visiting Professor
Sep 2008
Dec 2008
Bielefeld University Visiting Professor
Apr 2008
Sep 2008
Max Planck Institute in Bonn Visiting Professor
Nov 2002
Dec 2002
Mittag Leffler Institute, Sweden Guest Professor


Mar 1974
Mathematics, Graduate School, Division of Natural Science, The University of Tokyo
Mar 1972
Faculty of Science, Tokyo Institute of Technology

Committee Memberships

Apr 2017
Mathematics Education Society of Japan
Scientific Advisory Committee of the special project ''Periodic and Ergodic Spectral Problems'' at Isaac Newton Institute for Mathematical Sciences  Committee member
Program Committee (Geometry Section) of ICM 2014  member
Editorial committee of translation of ``Princeton Companion"  Chief editor
European Research Council  Panel member

Awards & Honors

Apr 2018
The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology, The Ministry of Education, Culture, Sports, Science and Technology
Winner: Toshikazu Sunada
Apr 2017
Fujiwara Hiroshi Prize for Mathematical Sciences
Winner: Toshikazu Sunada
Mar 2013
Publication Prize of Mathematical Society of Japan, Mathematical Society of Japan
Iyanaga Prize of Mathematical Society of Japan

Published Papers

From Euclid to Riemann and beyond
Proceedings for the conference "Geometry in History"      Feb 2017   [Refereed][Invited]
Topics on mathematical crystallography
T. Sunada
London Mathematical Society Lecture Note Series   436 475-519   2017   [Refereed][Invited]
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   Dec 2014   [Refereed]
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   Mar 2012
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   Jan 2012
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 ...


Geometric Aspects of Large Deviations for Random Walks on a Crystal Lattice
M. Kotani
RIMS Proceedings   1236 112-114   2001
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   [Refereed]
From Euclid to Riemann
44(6) 77-93   Mar 2016

Books etc

"Mathematical Gift, III"
Koji Shiga (Part:Joint Work)
American Mathematical Society   May 2005   
Topological Crystallography --With a View Towards Discrete Geometric Analysis
Springer   Dec 2012   ISBN:978-4-431-54176-9
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid's Elem...
From Riemann to Differential Geometry and Relativity
Toshikazu Sunada (Part:Joint Work, Generalized Riemann sums, p.457--479)
Springer   2017   
Geodesic flows and geodesic random walks
Toshikazu Sunada
Math. Soc. of Japan   1984   
Analysis on garphs and its applications
"P. Exner, J. P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev" (Part:Supervisor)
American Mathematical Society   Nov 2008   

Conference Activities & Talks

Isospectral manifolds [Invited]
Jun 1984   
Isospectral manifolds [Invited]
6th Differential geometry and differential equations   Jun 1985   
Lectures on twisted Laplacians [Invited]
Feb 1990   Tata Institute
Trace formulae in spectral geometry [Invited]
International Conference of Mathematics (ICM) in Kyoto   Aug 1990   
Ihara zeta function [Invited]
AMS-IMS-SIAM Summer Research Conference   1993   AMS-IMS-SIAM

Research Grants & Projects

Progress of discrete geometric analysis
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research (A)
Project Year: Apr 2015 - Mar 2019    Investigator(s): Toshikazu Sunada
Development of discrete geometric analysis
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research (B)
Project Year: Apr 2012 - Mar 2015    Investigator(s): Toshikazu Sunada
Development and applications of discrete geometric analysis
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research (B)
Project Year: Apr 2009 - Mar 2012    Investigator(s): Toshikazu Sunada
Study of non-commutative geometric analysis
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research (C)
Project Year: Apr 2006 - Mar 2008    Investigator(s): Toshikazu Sunada
Commutative and non-commutative Bloch theory
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research (A)
Project Year: Apr 2001 - Mar 2005    Investigator(s): Toshikazu Sunada