| 词条 | Toshikazu Sunada |
| 释义 |
|name = Toshikazu Sunada |image =Mr._Toshikazu_Sunada.jpg |caption = |birth_date = {{birth year and age|1948}} |birth_place = Tokyo, Japan |death_date = |death_place = |residence = |citizenship = |nationality = Japanese |ethnicity = Japanese |field = Mathematics (Spectral geometry and Discrete geometric analysis) |work_institutions = Nagoya University Tokyo University Tohoku University Meiji University |alma_mater = Tokyo Institute of Technology |doctoral_advisor = |doctoral_students = |known_for = |influences = |influenced = |prizes = 1987 Iyanaga Award of Mathematical Society of Japan 2013 Publication Prize of Mathematical Society of Japan 2017 Hiroshi Fujiwara Prize for Mathematical Sciences 2018 Prize for Science and Technology (the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology) 2019 the 1st Kodaira Kunihiko Prize |religion = |footnotes = }}{{Nihongo|Toshikazu Sunada|砂田 利一|Sunada Toshikazu|born September 7, 1948}} is a Japanese mathematician and author of many books and essays on mathematics and mathematical sciences. He is professor of mathematics at Meiji University, Tokyo, and is also professor emeritus of Tohoku University, Tohoku, Japan. Before he joined Meiji University in 2003, he was professor of mathematics at Nagoya University (1988–1991), at the University of Tokyo (1991–1993), and at Tohoku University (1993–2003). Sunada was involved in the creation of the School of Interdisciplinary Mathematical Sciences at Meiji University and is its first dean (2013–2017). Main workSunada'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 (1985), 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?" (see Hearing 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 (MSJ) 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 (the Commendation for Science and Technology by the Minister of Education, Culture, Sports, 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 (1988). One can see, in this work as well as the one above, how the concepts and ideas in totally different fields (geometry, dynamical systems, and number theory) 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 (2005). He named it the K4 crystal due to its mathematical relevance (see the linked article). 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 strong isotropy should not be confused with the edge-transitivity or the notion of symmetric graph; for instance, the primitive cubic lattice is a symmetric graph, but not strongly isotropic). 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 (Abel-Jacobi 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
References
9 : 1948 births|Living people|20th-century Japanese mathematicians|21st-century Japanese mathematicians|Geometers|Meiji University faculty|Tokyo Institute of Technology alumni|Tohoku University faculty|Nagoya University faculty |
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