Toshikazu Sunada

Toshikazu Sunada (Japanese砂 田 利 一, Toshikazu Sunada, born September 7, 1948 in Tokyo) is a Japanese mathematician who is engaged in, among others, with geometric Analysis and Analysis on graphs.

Life

Sunada studied from 1968 at the Technical University of Tokyo ( Tokyo Institute of Technology), among others, Koji Shiga and at the University of Tokyo, where he in 1974 Mikio Ise received his diploma (where he was examined by Kunihiko Kodaira ) and her doctorate in 1977. From 1974 he was a researcher at Nagoya University ( 1975 to 1977 also at the University of Tokyo), where he became assistant professor in 1982 and professor in 1988. From 1991 he was a professor at Tokyo University and from 1993 to Tohoku University, where he is professor emeritus since 2003. He is at Meiji University Professor since 2003. He is also the Meiji Institute for Advanced Study in Mathematical Sciences in Tokyo. He has been a visiting scientist at the IHES (1988 ), at the University of Bonn (1979 /80) and the Max Planck Institute for Mathematics in Bonn (2008), Humboldt University, Berlin (2008), the Isaac Newton Institute in Cambridge (2007 ), the Institute Henri Poincaré in Paris, the Mittag-Leffler Institute, the Academy of Sciences in Beijing, the MSRI, the Tata Institute of fundamental Research, the Philippines and Singapore.

He is co-editor of a Japanese magazine called mathematics Have fun with math (Nihon Hyoron -sha).

Work

He dealt with geometric analysis ( especially spectral geometry), complex geometry ( geometry of functions of several complex variables ), probability theory. Mid-1980s, he gave a general construction isospektraler manifolds, ie those with the same spectrum of the Laplacian. This was an important advance in the questions of Mark Kac problem to find manifolds, which are different in spite of the same spectrum ( Can one hear the shape of a drum? ). The problem was ( with methods of Sunada ) 1992 by Carolyn Gordon, Scott Wolpert, David Webb solved in a positive sense.

From Sunada comes a graph-theoretic interpretation of the Ihara zeta function ( by Yasutaka Ihara ), similar with an explicit formula of the Selberg zeta function (in this case, with the eigenvalues ​​of the adjacency matrix on the one hand and the length of closed cycles of the graph on the other side ). He also proved that the Riemann hypothesis for the Ihara zeta function of a ( contiguous k- regular ) graph is equivalent to saying that the graph is a Ramanujan graph with Atsushi Katsuda he gave an analogue of the Dirichlet theorem on primes in arithmetic consequences in the theory of dynamical systems, in consideration of the density of closed orbits of Anosov flows on compact manifolds, to a certain homology class. Sunada studied the asymptotic behavior of random walks on lattices. He also discovered a crystal lattice shape, the K4 crystal, which in its highly symmetrical behavior in terms of the equivalence of the orientations in space ( isotropy ) only with the diamond lattice in three dimensions and the honeycomb structure (hexagonal crystal lattice, realized in graphene ) in two dimensions comparable.

In 1987 he received the Prize of the Japanese Iyanaga Mathematical Society. He was invited speaker at the ICM 1990 in Kyoto (Trace Formulae in spectral geometry, with M. Nishio ).