# Sunada

Sunada's idea was taken up by C. Before he joined Meiji University in , he was professor of mathematics at Nagoya University — , at the University of Tokyo — , and at Tohoku University — 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 Sunada, Lecture on topological crystallography, Japan. Wolpert when they constructed a counterexample for Kac's problem.

Sunada, Rigidity of certain harmonic mappings, Invent. Wolpert when they constructed a counterexample for Kac's problem. Sunada's idea was taken up by C. Main work[ edit ] Sunada's work covers complex analytic geometry , spectral geometry , dynamical systems , probability , graph theory , and discrete geometric analysis. 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. Sunada, Closed orbits in homology classes, Publ. Sunada, Lecture on topological crystallography, Japan. Sunada, Unitary representations of fundamental groups and the spectrum of twisted Laplacians, Topology 28 , — A. Teplyaev , 77 , 51—86 K. Kotani as a graph-theoretic version of Albanese maps Abel-Jacobi maps in algebraic geometry. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. He named it the K4 crystal due to its mathematical relevance see the linked article. 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 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, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. 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. 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 Sunada, L-functions and some applications, Lect. Sunada, Trace formulae in spectral geometry, Proc. Selected Publications by Sunada[ edit ] T. Sunada, Albanese maps and an off diagonal long time asymptotic for the heat kernel, Comm. 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. Before he joined Meiji University in , he was professor of mathematics at Nagoya University — , at the University of Tokyo — , and at Tohoku University — Sunada, Homology and closed geodesics in a compact Riemann surface, Amer. Sunada, Riemannian coverings and isospectral manifolds, Ann. Sunada was involved in the creation of the School of Interdisciplinary Mathematical Sciences in Meiji University and is its first dean Sunada, Spectral geometry of crystal lattices, Contemporary Math.

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