Topological insulators and semimetals
Andrei Bernevig (Princeton University, USA)
I will review topological states of matter with specific emphasis on the symmetry-protected topological insulators in different dimensions. I will show how Majorana states can be realized at the end of topological chains with fermionic parity, as well as in vortex cores in 2D chiral superconductors. I will then show how some of the simplest tensor Braided categories come out of simple, intuitive physical arguments about braiding vortices. I will present a slew of topological insulators protected by time reversal, symmorphic, and then nonsymmorphic symmetries. At then end, I will present new work aiming to provide a complete and comprehensive classification of all topological insulators existent in crystals.