There are two kinds of scientific methodologies; a science of elements
and a science of logics. The former is the methodology to explore reductionism
like the elementary particle physics. The latter is the methodology to
explore universality of mathematical structure hidden behind various phenomena
of nature. Due to the excellent universal mathematical structure, topology
becomes a new leading principle of science in 21st century.
Our group constructs new science by combining the two methodologies complementally; the methodology for reductionism used in the condensed matter physics and the methodology to prove the universality of mathematical structure (topological science and technology). Therefore, we investigate various fields on the topological viewpoint.