Mathematical challenge to understand Materials structure

Motoko Kotani

Mathematical Institute

Tohoku University

m-kotani@m.tohoku.ac.jp

Materials is a complex system with hierarchical structure; namely materials consists of atoms, atoms form atomic clusters, atomic clusters from their networks, entangled networks form nano-structures. Therefore it is a challenge to understand relations between structures and functions of materials. I would like to discuss how mathematics, discrete geometric analysis, contributes in the challenges. Non-equilibrium materials, topological materials, carbon materials are our targets.