Introduction to topological insulators for mathematicians

The aim of this seminar is to explain our mathematician colleagues the physics and mathematics behind topological insulators. Topological insulators are states of matter where the vector bundle corresponding to the system is topologically nontrivial, e.g. having non-zero Chern number. (I will explain what "the vector bundle corresponding to the system" exactly means in this seminar.) Non-trivial topology has experimentally observable physical consequences, for example through quantized Hall conductivity. Topological insulators are an increasingly active area of research in condensed matter physics as it provides a new paradigm of states of matter which reflect the global topology of the system. In this seminar, I assume (physicists' level of) basic knowledge on differential geometry, such as fiber bundles and differential forms, but I try to be as pedagogical as possible for audience from both physics and mathematics backgrounds.