# Message from the Leader

Leader:TANDA,Satoshi

This center will create a new scope and an innovative field of study from the perspective of topology, a universal concept that is applicable across a wide range of fields. Incorporating mathematical science, applied physics, instrumentation and information technology, materials science, life science, and economics, we aim to build a true center of excellence for original and interdisciplinary research and education, both basic and applied. Topology is a field of study that assumes a soft rubber membrane and investigates properties that remain unchanged after continuous deformation without tearing or gluing. In the latter half of the 19th century, topology was a field of mathematics that focused solely on the connectivity of geometric structures and pursued the essential aspects of those geometric figures. Because it deals with geometric structures in general topology, since its inception, it has naturally been employed in fields of basic physics such as the general theory of relativity, which expresses deflected space and time, and quantum field theory. Since the latter half of the 20th century, with the discovery of the topological double helical structure of DNA as well as topological defects in liquid crystal and superconductors, it has been recognized anew that the concept of topology is also of great value in materials science. Furthermore, it has recently been shown that topology is also closely related to complex system studies that deal with thermal phase transitions, quantum phase transitions, other critical phenomena, as well as life science, carbon nano-tubes, various types of networks, and quantum information science that place importance on the relational aspects of systems. This is because topology, which is related to an extremely general scientific approach that pursues the relationships between localized properties and general properties, is required not only for mathematics and physics but also for biology, network theory, information theory, and economics.

There has been no attempt to understand such a wide range of scientific fields in a cross-sectional and comprehensive manner. The objective of this COE program is to experimentally and phenomenologically quantify the topological invariants that define structure using a combination of topology and dynamics as an approach to pursue the universal law underlying the whole of creation. The ultimate and major goal of this program is to draw theoretical conclusions and apply the new principles to a wide range of scientific fields. We intend to create a new system of research and to disseminate it from Hokkaido University.