Abstract:
 
Topological phases of matter are exotic states of matter with anyonic excitations such as the fractional quantum Hall (FQH)  liquids.  FQH liquids are described effectively by Witten's Chern-Simons theories.  More general topological phases of matter are described by unitary TQFTs or unitary braided tensor categories.  I will explain what are topological phases of matter, the mathematical models for topological phases of matter, their emergence from electrons and classification.  If time permits, the application to quantum computing.