ABSTRACT

Topological wave insulators exhibit topological properties that are immune to material defects, and they have received significant interest in physics and engineering due to their unusual robustness in the transportation of wave energy. In this talk, I will present our recent work on several fundamental mathematical problems in this topic. These include (i) Dirac point in periodic lattices; (ii) topological invariant and topologically protected edge modes in photonic crystals; (iii) spectral band gap optimization for topological photonic crystals.