In a variety of condensed matter systems, strongly interacting electrons can form a quantum liquid at low temperatures in which the electron fractionalizes into quasiparticles that carry fractions of the electron's charge, spin, and quantum statistics. Such phases of matter, referred to as topologically ordered quantum states, arise in the fractional quantum Hall effect and are believed to arise also in various frustrated quantum magnets. They also provide examples of dynamical gauge fields emerging from the collective properties of strongly interacting systems; their basic physics are intimately connected to quantum error correcting codes and the pursuit of fault-tolerant quantum computation. In this talk I will describe some developments in our understanding of topological defects and interfaces in such systems. One phenomena involves the possibility of direct conversion of an electron into a fractionalized quasiparticle upon crossing a topological interface. Another recent development is a general theory of topological defects that can be used to distinguish different symmetric topological orders, in some ways vastly generalizing the famous TKNN invariant for the quantum Hall effect.

Watch a recording of the talk here.