Video URL http://pirsa.org/21040009
We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different "symmetry-protected topological" phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.