- “Physics of the bulk-edge correspondence :its diversity and universality”
 - Focused lectures at the Chiba University, organized by Prof. T. Nakayama
 - July8-9 (2015)
 - Content of the lectures (pdf files are mostly in English)
 - 1. Introduction: [Talk file pdf]
 - 2. Quantum Hall effects: [Talk file pdf]
 - ♫ Gauge invariance and Laughlin argument: [Detail pdf]
 - 3. Electronic structue of silicene: [Talk file pdf]
 - 4. Berry phases & Chern number (their quantization): [Talk file pdf]
 - 5. Symmetry protection for topological phases: [Talk file pdf]
 - 6. Bulk-edge correspondence: [Talk file pdf]
 

