Toshikazu Sunada is a Japanesemathematician and author of many books and essays on mathematics and mathematical sciences. He is professor emeritus of both Meiji University and Tohoku University. He is also distinguished professor of emeritus at Meiji in recognition of achievement over the course of an academic career. Before he joined Meiji University in 2003, he was professor of mathematics at Nagoya University, at the University of Tokyo, and at Tohoku University. Sunada was involved in the creation of the School of Interdisciplinary Mathematical Sciences at Meiji University and is its first dean. Since 2019, he is President of Mathematics Education Society of Japan.
Main work
Sunada's work covers complex analytic geometry, spectral geometry, dynamical systems, probability, graph theory, discrete geometric analysis, and mathematical crystallography. Among his numerous contributions, the most famous one is a general construction of isospectral manifolds, which is based on his geometric model of number theory, and is considered to be a breakthrough in the problem proposed by Mark Kac in "Can one hear the shape of a drum?". Sunada's idea was taken up by Carolyn S. Gordon, David Webb, and Scott A. Wolpert when they constructed a counterexample for Kac's problem. For this work, Sunada was awarded the Iyanaga Prize of the Mathematical Society of Japan in 1987. He was also awarded Publication Prize of MSJ in 2013, the Hiroshi Fujiwara Prize for Mathematical Sciences in 2017, the Prize for Science and Technology in 2018, and the 1st Kodaira Kunihiko Prize in 2019. In a joint work with Atsushi Katsuda, Sunada also established a geometric analogue of Dirichlet's theorem on arithmetic progressions in the context of dynamical systems. One can see, in this work as well as the one above, how the concepts and ideas in totally different fields are put together to formulate problems and to produce new results. His study of discrete geometric analysis includes a graph-theoretic interpretation of Ihara zeta functions, a discrete analogue of periodic magnetic Schrödinger operators as well as the large time asymptotic behaviors of random walk on crystal lattices. The study of random walk led him to the discovery of a "mathematical twin" of the diamond crystal out of an infinite universe of hypothetical crystals. He named it the K4 crystal due to its mathematical relevance. What was noticed by him is that the K4 crystal has the "strong isotropy property", meaning that for any two vertices x and y of the crystal net, and for any ordering of the edges adjacent to x and any ordering of the edges adjacent to y, there is a net-preserving congruence taking x to y and each x-edge to the similarly ordered y-edge. This property is shared only by the diamond crystal . The K4 crystal and the diamond crystal as networks in space are examples of “standard realizations”, the notion introduced by Sunada and Motoko Kotani as a graph-theoretic version of Albanese maps in algebraic geometry. For his work, see also Isospectral, Reinhardt domain, Ihara zeta function, Ramanujan graph, quantum ergodicity, quantum walk.
Selected Publications by Sunada
T.Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Mathematische Annalen235, 111–128
T.Sunada, Rigidity of certain harmonic mappings, Inventiones Mathematicae51, 297–307
J.Noguchi and T.Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, American Journal of Mathematics104, 887–900
T.Sunada, Riemannian coverings and isospectral manifolds, Annals of Mathematics121, 169–186
T.Sunada, L-functions and some applications, Lecture Notes in Mathematics1201, Springer-Verlag, 266–284
A.Katsuda and T.Sunada, Homology and closed geodesics in a compact Riemann surface, American Journal of Mathematics110, 145–156
T.Sunada, Unitary representations of fundamental groups and the spectrum of twisted Laplacians, Topology28, 125–132
A.Katsuda and T.Sunada, Closed orbits in homology classes, Publications Mathématiques de l'IHÉS71, 5–32
M.Nishio and T.Sunada, Trace formulae in spectral geometry, Proc. ICM-90 Kyoto, Springer-Verlag, Tokyo,, 577–585
T.Sunada, Discrete geometric analysis, Proceedings of Symposia in Pure Mathematics, 77, 51–86
K.Shiga and T.Sunada, A Mathematical Gift, III, American Mathematical Society
T.Sunada, Lecture on topological crystallography, Japan Journal of Mathematics7, 1–39
T. Sunada, Topological Crystallography, With a View Towards Discrete Geometric Analysis, Springer, 2013, 978-4-431-54177-6
T. Sunada, Generalized Riemann sums, in From Riemann to Differential Geometry and Relativity, Editors: Lizhen Ji, Athanase Papadopoulos, Sumio Yamada, Springer, 457-479
